Quadratics and polynomials
Factoring simple expressions
None
How to factor a quartic binomial with two variables by taking a common factor (example)
Sal factors 4x^4y+8x^3y as 4x^3y(x+2).
Discussion and questions for this video
Do you understand English? Click here to see more discussion happening on Khan Academy's English site.
 Factor out the greatest common factor.
 And the expression they give us is 4x to the fourth y plus 8x
 to the third y.
 When they say to factor out the greatest common factor they're
 essentially telling us, find the greatest common factor of 4x
 to the fourth and 8x to the third y
 and factor it out of this expression.
 Or kind of undistribute it.
 And to find that greatest common factor
 and I always put it in quotes when
 we speak in algebraic terms.
 Because we don't really know what
 x and y are, whether they're positive or negative
 or whether they're greater than or less than 1.
 So it's not always going to be the greatest absolute number.
 But it's the greatest in it contains the most
 terms of these two expressions, these two monomials.
 So if we were to essentially factor out 4x to the fourth y
 it would look like this.
 We would do the prime factorization
 of 4, which is just 2 times 2, times x to the fourth, which
 is x times x times x times x, times y.
 We just expanded it out as a product
 of its basic constituents.
 Now let's do the same thing for 8
 I'll color code it 8x to the third.
 Let me do it in similar colors.
 So in this situation we have 8x to the 1/3 y.
 So the prime factorization of 8 is 2 times 2 times 2.
 It's 2 times 2 times 2.
 Prime, or I should say the factorization of x
 to the third, or the expansion of it,
 is just times x times x times x. x
 multiplied by itself three times.
 And then we are multiplying everything by a y here,
 times y.
 So what factors are common to both of these?
 And we want to include as many of them as possible
 to find this greatest common factor.
 So we have two 2's here, three 2's here.
 So we only have two 2's in common in both of them.
 We have four x's here, only three x's here.
 So we only have three x's in common.
 Three x's and three x's.
 And we have a y here and a y here.
 So y is common to both expressions.
 So the greatest common factor here is going to be 2 times 2.
 So it's going to be 2 times 2 times x times x times x times
 y.
 Or 4x to the third y.
 So this is what we want to factor out.
 So that means we can write this thing as if we factor out
 a 4x to the third y, where essentially we
 have to divide each of these by 4x to the third.
 We're factoring it out.
 So let me rewrite this.
 So this is 4x to the fourth y plus 8x to the third y.
 And we're going to divide each of these by 4x to the third y.
 And hopefully this makes sense to you.
 If we were to multiply this out, we
 would distribute this 4x to the third y on each terms.
 And then it would cancel with the denominator.
 You would have the same thing in the numerator and denominator.
 And then you would get this expression over here.
 So hopefully this makes sense that these
 are the exact same expression.
 But when you write it this way, then it
 becomes pretty clear that this is 4x to the third y.
 And then you just simplify each of these expressions.
 4 cancels with 4. x to the fourth
 divided by x to the third is x.
 y divided by y is just 1.
 So you have x plus 8 divided by 4 is 2.
 x to the third divided by x to the third is 1.
 Y divided by y is 1.
 So x plus 2.
 Another way to see what's left over when you factor it out
 is if you were to take out the common factor.
 So we took out this and this.
 What was left over in 4x to the fourth y
 when we took this stuff out?
 When we undistributed it?
 Well, the only thing that was left
 was this x right over here.
 Let me do that in another color.
 The only thing that was left was this x.
 So that's why we just have that x over there.
 When we factored everything out of the 8x to the third y
 we factored all this other stuff out.
 We factored out 4x to the third y.
 We factored it out, so all we had left was the 2.
 Now in general, you don't always have
 to go through this process.
 You could have done it this way, but this really hopefully makes
 it clear exactly what we're doing.
 You could have said, look, 4x to the fourth y
 plus 8x to the third y.
 You could have said, well let's see,
 the largest number that's divisible into both 4
 an 8 is 4.
 So let's factor out a 4 out here.
 The largest multiple of x that's divisible into x to the fourth
 and x to the third, well that's going to be x to the third.
 And you put an x to the third out here.
 And you say, well, the largest thing
 that's divisible both into y and y is just y.
 So you could have done it a little bit faster in your head.
 So you factor out a 4x to the third
 and you say, OK, if I take out a 4 out of here,
 then this becomes a 1.
 If I take an x to the third out of x to the fourth
 I'll just have an x left over.
 And then if I take a y out of the y then
 I just have a 1 there.
 So this term becomes x.
 And then if I take a 4x to the third y
 out of here, if I take a 4 out of an 8
 I just have a 2 left over.
 If I take an x to the third out of x to the third,
 that's just 1.
 If I take y out of y, that's just one.
 So I'm just left with x plus 2.
 Eventually you'll just do this in your head a little bit
 faster.
 But hopefully this makes everything clear.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

Have something that's not a question about this content? 
This discussion area is not meant for answering homework questions.
Why don't you add the ones from the xs and ys?
Because one times something is just that something. Writing 1x is the same as writing x.
1*1*1*1*1*1*1*1*x is still x
Since each quotient is a monomial, all of the terms within that monomial are being multiplied together, not added as I assume you are thinking. Therefore, the value would not change because 1 times any number is that number.
because its not possible to add them because u don't know what they are, if u multiply them is become xys^2
you dont do this because they are not like terms the way i remember is Cheese Lettuce and Tomatoes Combine Like Terms
What is the difference between the LCM , LCD and GCF ?
LCM is the lowest common multiple. This means that you find the smallest number that can be divided by both. For example, the LCM of 4 and 3 is 12, and the LCM of 3 and 6 is 6.
LCD is the lowest common denominator. This is useful when adding or subtracting fractions, as you need a LCD to add/subtract them. You would find it in the same method that you would find the LCM. for example, the LCD of 1/2 and 1/3 would be 6. You would change the denominator of both fractions to six and then alter the numerator by the same factor as the denominator. So, 1/2 would become 3/6 and 1/3 would become 2/6. They can now be added or subtracted.
GCF is the largest number that both numbers can be divided by. There really isn't a simple way to find it, but you just try to find the largest common factor to both numbers. For example, the GCF of 12 and 18 is 6, and the GCF of 24 and 25 is 1.
hope this helps!
LCD is the lowest common denominator. This is useful when adding or subtracting fractions, as you need a LCD to add/subtract them. You would find it in the same method that you would find the LCM. for example, the LCD of 1/2 and 1/3 would be 6. You would change the denominator of both fractions to six and then alter the numerator by the same factor as the denominator. So, 1/2 would become 3/6 and 1/3 would become 2/6. They can now be added or subtracted.
GCF is the largest number that both numbers can be divided by. There really isn't a simple way to find it, but you just try to find the largest common factor to both numbers. For example, the GCF of 12 and 18 is 6, and the GCF of 24 and 25 is 1.
hope this helps!
I dont get the difference of the Greatest Common Factor (GCF) and the Least Common Denaminator (LCD) ? is it the same formula to find it ?
No, you are only using GCF to factor these types of polynomials. Look up GCF and LCM on Khan Academy videos and you will see the difference.
well, LCM is the first multiple that is common in both numbers*
GCF is the largest factor that divides BOTH the numbers
the procedure for finding the GCF is different from LCM finding
if you prime factorize both the numbers, the PRODUCT OF ALL the COMMON factors is the GCF, while on the other hand LCM is the product of all the common factors and the remaining factors
eg: GCF and LCM of 12 and 9
12 = 2 * 2 * 3 and 9 = 3 * 3 here the common factor is 3 and is common only ONCE.
(HCF IS 3) now multiply 3 * 2 * 2 * 3 (i'm taking 3 only once because it is common only once) 36 is the lcm
GCF is the largest factor that divides BOTH the numbers
the procedure for finding the GCF is different from LCM finding
if you prime factorize both the numbers, the PRODUCT OF ALL the COMMON factors is the GCF, while on the other hand LCM is the product of all the common factors and the remaining factors
eg: GCF and LCM of 12 and 9
12 = 2 * 2 * 3 and 9 = 3 * 3 here the common factor is 3 and is common only ONCE.
(HCF IS 3) now multiply 3 * 2 * 2 * 3 (i'm taking 3 only once because it is common only once) 36 is the lcm
No, you're thinking of the LCM (Least Common Multiple) .
The LCD is the LCM of the denominators (assuming the fractions are already in their simplest form)
The LCD is the LCM of the denominators (assuming the fractions are already in their simplest form)
umm i dont think so
I have to do this x4x2 of course the 4 And 2 are exponents the book said that if possible factor the polynomial completely ?
Just factor out x^2 from each term in the original polynomial, which becomes x^2(x^21). Factoring further it becomes x^2(x+1)(x1). Hope this helps.
Another way to try this one is using substitution, which can be helpful for tricky factoring. An easy way to tackle this problem is to substitute the lowest exponent value of x (in this case x^2) as another variable, such as y. Then, at the very end of the problem, we can put all our yvariables back into x's. So, set x^2 = y. Now the polynomial becomes y^2  y^1. Factor out a y^1. Now the polynomial becomes: y(y1). This cannot be factored any further. Now put back the x's, noting that y=x^2. So, the polynomial becomes: x^2(x^2  1) This can be factored further: x^2(x+1)(x1)
Another way to try this one is using substitution, which can be helpful for tricky factoring. An easy way to tackle this problem is to substitute the lowest exponent value of x (in this case x^2) as another variable, such as y. Then, at the very end of the problem, we can put all our yvariables back into x's. So, set x^2 = y. Now the polynomial becomes y^2  y^1. Factor out a y^1. Now the polynomial becomes: y(y1). This cannot be factored any further. Now put back the x's, noting that y=x^2. So, the polynomial becomes: x^2(x^2  1) This can be factored further: x^2(x+1)(x1)
My friend who has all As told me to put can't be factored for an answer
Thanks i got what you're saying but didnt U mean i had to square it or am i just off base can u also help me with this one m^25m35
I'm trying to understand how to factor polynomials using GCF but I still don't get it. Can you help me understand it?
Andria,
Welcome to Khan Academy.
Try watching the vidoe again. Sometimes it takes a couple times for things to click.
Sal explains it much better than I can.
You are using the Distributive Property. x*(a+b) = xa +xb, but in reverse that is:
xa + xb = a*(a+b).
You want to find the most common factors that make up the x. And this GCF is then placed outside the parenthesis and everything else is left inside the parenthesis.
If you had just numbers such as
2*3*5*5*7 + 2*3*9
you would factor out everything that is common to both. In this case 2*3 and place that outside the parenthesis so you would get
2*3(5*5*7 + 9).
If instead they were letters and numbers such as
x*x*y*5*3 + x*y*y*5*2
You would still find the all of the common factors, in this case x, y and 5 and place them outside the parenthesis
x*y*5(?+?)
and leave everytning else inside
x*y*5(x*3 + y*2)
I hope that helps
Welcome to Khan Academy.
Try watching the vidoe again. Sometimes it takes a couple times for things to click.
Sal explains it much better than I can.
You are using the Distributive Property. x*(a+b) = xa +xb, but in reverse that is:
xa + xb = a*(a+b).
You want to find the most common factors that make up the x. And this GCF is then placed outside the parenthesis and everything else is left inside the parenthesis.
If you had just numbers such as
2*3*5*5*7 + 2*3*9
you would factor out everything that is common to both. In this case 2*3 and place that outside the parenthesis so you would get
2*3(5*5*7 + 9).
If instead they were letters and numbers such as
x*x*y*5*3 + x*y*y*5*2
You would still find the all of the common factors, in this case x, y and 5 and place them outside the parenthesis
x*y*5(?+?)
and leave everytning else inside
x*y*5(x*3 + y*2)
I hope that helps
Well, in the video, it never says that you should subtract the exponents when you find your GCF, because I was told that you should subtract the exponents. I understand everything else, but that part of the video when he uses the GCF. Does anybody know the answer to my question?
you aren't supposed to subtract the exponents
At 2:45, why does he divide by 4x^3 y?
Because 4 is the greatest common factor between the numbers in each term, the two terms share the variable x and you always have to take the smallest exponent so you get x^3, and the two terms also share the variable y (like before you take the smallest exponent) so you get just y. I hope this makes sense.
At 5:09 he says it as if he is subtracting, how does taking a 4 out of an 8 result in a 2? Is he saying we are dividing? Then at 4:57 why is there nothing resulted instead of a 1?
You divide the coefficient to divide (which is what the lesson is, basically), and you subtract exponents to divide, so Sal did want that two, he just misspoke when talking about his operations
Sal made a mistake there. 84=4
It's not subtracting. He is using division.
how would you use this method when you have a problem like: 9x^2y^3 + x^2y^2/ 2x^3y^4 when its in that fraction form and you have to simplify using GCF. How can I find a video on here that shows problems like this or where to find out how to solve problems like this one?
some equations can't be factorised by finding a common factor, for that you will have to use the cross method, completing the square or the quadratic equation.
what is the greatest common factor of 70yx80y
10y
10 is the greatest factor that they share and they both share a y
10 is the greatest factor that they share and they both share a y
My problem is 14x^2 + 55x  21 Help! I'm clueless.
Wait, does factoring out GCF the same as just normal factoring?
Would the answer be the same if the question asked "factor 4x^4 y+8x^3 y"?
Would the answer be the same if the question asked "factor 4x^4 y+8x^3 y"?
Yes, it's the same thing. When people ask you to factor something, you can just assume that they mean factor out the GCF.
can you help me factor x2  5xs  24s2
x^2  5xs  24s^2
Think of this similar problem:
x^2  5x  24
= (x8)(x+3)
Your problem is almost the same, just add letter s:
x^2  5xs  24s^2
= (x8s)(x+3s)
Think of this similar problem:
x^2  5x  24
= (x8)(x+3)
Your problem is almost the same, just add letter s:
x^2  5xs  24s^2
= (x8s)(x+3s)
a^2+1516 factor the following
Simplify this question of 2/3(30+1) =
2/3 (30 + 1) =
Use the distributive property:
20 + (2/3) = 20 2/3 or 62/3
or
1. Complete the operation on the inside of the parenthesis first, and then multiply.
2/3 ( 30 + 1)
2/3 (31) = 20 2/3 or 62/3
Hope this helps! Terrell
Use the distributive property:
20 + (2/3) = 20 2/3 or 62/3
or
1. Complete the operation on the inside of the parenthesis first, and then multiply.
2/3 ( 30 + 1)
2/3 (31) = 20 2/3 or 62/3
Hope this helps! Terrell
Is there another way to say Greatest Common Factor?
Some people call it the H.C.F (Highest Common Factor).
maybe u could also say largest common factor (LCF) or biggest (BCF)
how do you this problem 5x50
Answer: 5(x10)
Solution:
Think about this way what is their GCF?
If we factor 5 we get 5 and 1. and when we factor 10 we get 2 and 5. So their GCF is 5. Now that we know the GCF, we factor it out to get 5(x10).
Solution:
Think about this way what is their GCF?
If we factor 5 we get 5 and 1. and when we factor 10 we get 2 and 5. So their GCF is 5. Now that we know the GCF, we factor it out to get 5(x10).
What is
x2 − 5x − 6?
x2 − 5x − 6?
I assume you mean x^2  5x  6 and "what is" is asking for the solution to the equation.
We can solve using the quadratic equation!
[b ± √(b^2  4ac)] / 2a
FYI √ is square root and ± is plus or minus
If you don't know what a, b, and c are, that's okay. a is coefficient of x^2, b is the coefficient of x, and c is the last number. This equation only works with equations like these.
a = 1
b = 5
c = 6
(5) = 5
{5 ± [√ (5^2)  4(1)(6)] } ÷ 2(1)
{5 ± [√ 25 + 24]} ÷ 2
{5 ± √49} ÷ 2
{5 ± 7} ÷ 2
5 + 7 = 12
5  7 = 2
12 ÷ 2 = 6
2 ÷ 2 = 1
So your xintercepts (solutions) are at 6 and 1.
In other words the final factored form is
(x6)(x+1) < This is the answer
You're probably thinking, "You said the answers were 6 and 1, but you put x6 and x+1. Yes I did! That's the correct format. When you set x to 6 in the equation, you get zero and same if you put in 1. Hope this helps :)
We can solve using the quadratic equation!
[b ± √(b^2  4ac)] / 2a
FYI √ is square root and ± is plus or minus
If you don't know what a, b, and c are, that's okay. a is coefficient of x^2, b is the coefficient of x, and c is the last number. This equation only works with equations like these.
a = 1
b = 5
c = 6
(5) = 5
{5 ± [√ (5^2)  4(1)(6)] } ÷ 2(1)
{5 ± [√ 25 + 24]} ÷ 2
{5 ± √49} ÷ 2
{5 ± 7} ÷ 2
5 + 7 = 12
5  7 = 2
12 ÷ 2 = 6
2 ÷ 2 = 1
So your xintercepts (solutions) are at 6 and 1.
In other words the final factored form is
(x6)(x+1) < This is the answer
You're probably thinking, "You said the answers were 6 and 1, but you put x6 and x+1. Yes I did! That's the correct format. When you set x to 6 in the equation, you get zero and same if you put in 1. Hope this helps :)
how can i solve a^3 +6a^211a
your right the a= A(A*2+6A11)
Well,A^3 = A * A * A
and 6A^2 = 2 * 3 * A * A
and 11A = 11 * A
so we have as a common factor, A
So, It turns into A(A^3/A + 6A^2/A  11A/A)
= A(A^2 + 6A  11)
(I may be wrong)
and 6A^2 = 2 * 3 * A * A
and 11A = 11 * A
so we have as a common factor, A
So, It turns into A(A^3/A + 6A^2/A  11A/A)
= A(A^2 + 6A  11)
(I may be wrong)
what if it is a 2 instead of a 4 or higher? would you say 1 x 1 x whatever...
If there were a two in the first polynomial instead of a four (2x^4y instead of 4x^4y), you would factor it out as: 2*x*x*x*x*y.
1*1*x*x*x*x*y would just be x^4y, the ones are redundant.
1*1*x*x*x*x*y would just be x^4y, the ones are redundant.
I don't get it why 4x3y?
These videos are great, but I'm just wondering one thing: why did Sal say stuff like X+X+X+X when he could have said X times 4? I mean, I think a good number of us viewers know that 4x=x times 4.
He didn't say x+x+x+x, he said x TIMES x times x times x. Very different.
X + X + X + X is equal to 4X.
X * X * X * X is equal to x^4.
X + X + X + X is equal to 4X.
X * X * X * X is equal to x^4.
I think that many viewers DO understand that 4x=x times 4. However, some may not. If a student has a "gap" in their understanding, this extra explanation might help to fill it. Also, sometimes it helps to understand the concept when it is explained further.
are there any more example videos on this subject
trying to solve this equation: x^34x^2+4x16
Explain how to factor a monomial GCF out of terms in a polynomial
question what do you do when you have a problem with a variable squared a number and variable and then a number by itself?
At 2:29, how do you get 4x^3y
80+65
distributive property write each sum as a product of the GCF of the two numbers
distributive property write each sum as a product of the GCF of the two numbers
Austin
Break each number into its primes
80 = 2*2*2*2*5
65 = 5*13
The only common factor is 5 so factor out a five
5(16+13)
I hope that helps make it click for you.
Break each number into its primes
80 = 2*2*2*2*5
65 = 5*13
The only common factor is 5 so factor out a five
5(16+13)
I hope that helps make it click for you.
where do you find simplifying
look it up in the search box
How do I factor a polynomial with a GCF of 1?
Perhaps like this;
4y13y_2_
= 1y(413y)
4y13y_2_
= 1y(413y)
how would you solve 80xy  245x^2
1. Identify the common factors of 80xy and 245x^2
Factors of 80xy are 5 * 2 * 2 * 2 * 2 * x * y
Factors of 245x^2 are 5 * 7 * 7 * x * x
2. Take the common elements out of this list of factors and determine the number to factor out. Here the number is 5x.
3. Determine how many times 5x goes into 80xy and 245x^2 by dividing these numbers by 5x, then write your result in parentheses: 5x(16y  49x)
5x(16y  49x) is your answer
Factors of 80xy are 5 * 2 * 2 * 2 * 2 * x * y
Factors of 245x^2 are 5 * 7 * 7 * x * x
2. Take the common elements out of this list of factors and determine the number to factor out. Here the number is 5x.
3. Determine how many times 5x goes into 80xy and 245x^2 by dividing these numbers by 5x, then write your result in parentheses: 5x(16y  49x)
5x(16y  49x) is your answer
This confused me way more about gcf! D:
Can you please explain how do i factorize 8(4x+5y)2 +12(4x+5y)
the 2 in above expression is square ..
the 2 in above expression is square ..
If I have a more complicated expression that becomes 11g(2^2+x^2) how do I simplify that? I was told only when you are subtracting two squares you can use (a+b)(ab)
not always
you can use (a+b)(ab)
you can use (a+b)(ab)
At 3;51 my teacher told me something entirely different. i don't understand either onecan you show me a simpler
how do you factor by grouping trinomials?
Do you have a solution for factors of 9 than GCF and factor of 12 than GCF if you do please tell me
at 2:40 why do you divide?
how can i factor with two terms?
Is there anyway I can find a video related to the FOIL method? Please anyone respond.
Ya just type in the foil method in the search box
At 5:13, how do you get 2 if you take a four out of an 8?
Do you have any videos that tell how to do this when you have a polynomial with four terms, our math teacher shows what you're doing when you have two terms, but when there are four or more, she shows something COMPLETELY different. Thanks :)
There are several factoring techniques. Remove a GCF from a polynomial can be done with a polynomial of 2 or more terms. However, not all polynomials have GCF factors. So, other techniques are needed. There is a technique called grouping this is used for a polynomial of 4 terms. Check out video titled: Example: Basic grouping.
Is there a more simple explanation to this video? Im only in 6th grade and have a test
20140909T01:02:09Z
by
Anonymous
i have a lot of trouble with geometry triangle congruency can u plz help me!
You should really ask this question in a geometry lesson, where it would be more ontopic. But, since I'm here…
Triangles are congruent when the angles that make them up are the same _and_ all their sides are the same length as one another. Orientation or location of the triangles do not matter, so long as they are the same size and their angles match.
If the angles are the same but they are different sizes, then they are called _similar_ triangles.
If the triangles are merely described by coordinates on a Cartesian plane, then my advice is to go ahead and draw them out or use a computer to graph them, and then physically measure the sides and angles. You can use distance formulas and the Pythagorean theorem to get the answer, of course, but in my opinion that is frequently an unnecessary use of energy and time.
Triangles are congruent when the angles that make them up are the same _and_ all their sides are the same length as one another. Orientation or location of the triangles do not matter, so long as they are the same size and their angles match.
If the angles are the same but they are different sizes, then they are called _similar_ triangles.
If the triangles are merely described by coordinates on a Cartesian plane, then my advice is to go ahead and draw them out or use a computer to graph them, and then physically measure the sides and angles. You can use distance formulas and the Pythagorean theorem to get the answer, of course, but in my opinion that is frequently an unnecessary use of energy and time.
ples dont delet this coment
I have different answer for question find GCF for 4x^4y+8x^3y =4xy(x^3+2x^2)
ok, but what do you do when 4x^48x^3y? (subtracted)
On one of the mastery challenges, it says to use this same method to rewrite the expression 60+44 as the product of the greatest common factor of 60 and 44 and the sum of the remaining numbers. How do you do that exactly.
60 = 2 * 2 * 3 * 5 and 44 = 2 * 2 * 11 so the GCF = 2 * 2 = 4
So rewrite 60 + 44 as 4*(15 + 11)
So rewrite 60 + 44 as 4*(15 + 11)
how do you factor x^336? Im having trouble.
your gonna have to figure it out
x times x times x 36, if thats what your looking for
when two or more numbers are fractions, im presuming only fractions and zero are considered factors, is that right?
wasn't this vid different a few days ago?
why do we hae to do Gfc
This video is very nice and informative 😀
What is the steps i take is i have to factor a fraction out instead of a whole number? I.E. (1/2y^2 9/2y 11) I can get as far as 1/2(y^29y*****) I dont know if i factor a 1/2 from the 11 or not.
Of course you factor 1/2 from the 11. Why would you factor it out of the first two terms but not the last one? What is 11 divided by 1/2?
why cant you use 4 as the GCF?
Well you can if the two numbers were 4 and some multiple of 4 but in this case, the numbers involve variables so you have to account for the variables as well as the numbers you are trying to find the greatest common factor.
Question: Pam had two pieces of cloth the same length. She cut the first one into 8 equal parts. She cut the second one into 12 equal parts. How many parts from the second piece equal the same length as 4 parts from the first.
Suppose you have a question like y^3 +y^2 y, won't the GCF be y^3?
No, it might be more clear to you, if you would write power as multiplication:
y*y*y + y*y  y. If you look at each of those numbers, the smallest number has only one y, so you can factor only y: y(y^2+y+1)
GCF is y.
y*y*y + y*y  y. If you look at each of those numbers, the smallest number has only one y, so you can factor only y: y(y^2+y+1)
GCF is y.
At the very end of the video he said if you take a 4 out of an 8 you get a 2, am i missing something or was he not using subtraction?
Not subtraction, but division. If you take a factor of 4 out of 8 you get 2, because 2 times 4 equals 8.
What is the fastest way to factor any problem. EX: Polynomials, Trinomials, Binomials Ect.
Thanks, Herobrine
Thanks, Herobrine
Start by factoring out the Greatest Common Factor, then it depends on the makeup of the problem to decide whether it can be factored or which method to use. Sorry no better answer here.
OK, so I understand how to factor binomials, but what exactly is the point. When would this be needed?
i have a question...when a math prob is like this: 6y^3 (to the power of..) do they mean to put 2 'y's' or three extra?
At 1:49 seconds, Sal goes through the numbers and variables, but what if you have more than one "2" left? and could someone elaborate on how to write out the answer?
can you use a gcf calculator to find gcf because i found a website with a gcf calculator. This is the website: http://www.mathsisfun.com/greatestcommonfactortool.html.
You could, but it wouldn't work for the variables like x and y.
For example, if you typed in 5x and 15x, they would have no idea what to do and they wouldn't give you an answer. But it would work for the numbers alone.
For example, if you typed in 5x and 15x, they would have no idea what to do and they wouldn't give you an answer. But it would work for the numbers alone.
The GCF of two numbers x and y is 3. Can you predict the GCF of 4x and 4y? Explain your answer.
12, since you multiplied both by 4, that would be part of the GCF.
For example if I where to have 3x squared 3x+60 and it asked me find the GCF of the expression. Then factor the expression. How would I do this because it is different then simply factoring a quadratic expression
Hi, it is probably just 3 as the GCF: 3( x^2 x +20 ). 3 goes into all the coefficients, and we can't take out any x's because 60 doesn't have one.
how would u solve this problem
75x^5y and 135x^2y^3
75x^5y and 135x^2y^3
Factor it out? 75x^5y+135x^2y^3
=> 15x^2y(5x^3+9y^2)
=> 15x^2y(5x^3+9y^2)
What's the difference between HCF, GCF, GCD and HCD?
HCF is the same as GCF, and GCD is the same as HCD.
Highest (H) is exactly the same as Greatest (G) but you'll typically see G used more often.
Highest (H) is exactly the same as Greatest (G) but you'll typically see G used more often.
i still dont get this pls help : /
Watching earlier videos helps a lot too. Reading other people's questions and answers on the videos help a lot too.
Watch the video one more time and play close attention. That helps for me.
completely factor the polynomial.
4x^3+12x^2+4x+12
4x^3+12x^2+4x+12
how would you factor the equation 9x^3  3x^2  3x +1 = 0?
So first, Factor any constants out of the polynomial
4(x^3+3x^2+x+3)
Now, use a rarely used factoring method: grouping.
4(x^3+x+3x^2+3)
Now realize that if you factor an x out of the first two terms and 3 out of thast two, they become the same thing.
4(x(x^2+1)+3(x^2+1))
Now, you have x of something and 3 of the same something, so add them together to get 3+x of something.
4(x+3)(x^2+1)
And we're done!
Sal
4(x^3+3x^2+x+3)
Now, use a rarely used factoring method: grouping.
4(x^3+x+3x^2+3)
Now realize that if you factor an x out of the first two terms and 3 out of thast two, they become the same thing.
4(x(x^2+1)+3(x^2+1))
Now, you have x of something and 3 of the same something, so add them together to get 3+x of something.
4(x+3)(x^2+1)
And we're done!
Sal
Find GCF of 48, 140
48 =2x2x2x2x3
140 = 2x7x2x5
They only share a two twos, so 4 is the GCF of 48 and 140.
140 = 2x7x2x5
They only share a two twos, so 4 is the GCF of 48 and 140.
Factoring trinomials
How can GCF be used to factor a trinomial
at 0;38 sal says this monomial isn't it binomial? because it has two terms,,
He says "of these _two_ monomials" (emphasis mine). A binomial is made up of two monomials.
How to use zeros to write a polynomial function
Can you view ur words a little bit I can't see them
I have to find the lcm and gcf of xy^2 x xy^ 7. How do I do this and what impact does the negative seven have on the answer?
I have watched this video a few times. Every time I think I have it down I get thrown off. Can someone please help me understand how to factor polynomials using GCF?
i have a problem where i cant find the gcf of 4 and 5.
you can't factorise some things
I'm a bit confused; not about the actual solving, but the meaning of finding the GCF and factoring. When I was younger, I learned that the GCF is basically the biggest term that can go into a set of numbers. For example:
GCF of 8 and 10 is 2
But this video explains it further with more "complications". For example:
GCF of 8 and 10 is 2(4+5)
So could someone tell me which one is the "real" GCF?
GCF of 8 and 10 is 2
But this video explains it further with more "complications". For example:
GCF of 8 and 10 is 2(4+5)
So could someone tell me which one is the "real" GCF?
Hello, maybe I can help. In your first set, they are just 2 separate numbers, 8 & 10. In the second example you give it is an expression, 8+10, and not just 8 & 10. It may not make sense what the difference is, but remember that we are working with variables whose values we don't know. What is the GCF of 8 and 10? It is 2 as you said already. What is the GCF of 8x+10? It is 2, and the factored expression then becomes 2(4x+5). Another way to think of the difference is that your first example is to teach you how to find the GCF, while the second is the _application_ of the GCF to _factor_ an expression.
Where is the exercise?
How do you factor 10x^2+25x
you would take out the GCF between 10 and 25. The multiples of 10 are 1,2,5,10 and the multiples of 25 are 1,5,25. The greatest one that has the same multiple in each of the number is 5. So you would factor out the 5 which the equation would 5(2x^2+5). This is the furthest you can go unless you were to factor out by solving a square.
At 0:30, what does he mean by "greatest absolute number"?
So, I get how to find the GCF of a polynomial, but how do you find the greatest common monomial factor of a polynomial? Is it sort of the same thing? Or is it different?
Ok so what about an equation with two variables in a question like:
8u^2  2v^2
8u^2  2v^2
The variables aren't common to the terms, so the most you can factor out is the constant. 2, in this case:
2(4u^2  v^2)
2(4u^2  v^2)
Why is it 2.2
I am having math trouble with my math homework with GCF can anyone help me it`s 15y^2240 and I need factor by using GCF please help me.
The GCF is, in other words, is the greatest number that goes into both 15 and 240. In this case the GCF is 15. It goes into both 15 and 240. So
15y^2240. Factor out 15.
15(y^216). This equals to 15(y4)(y+4).
15y^2240. Factor out 15.
15(y^216). This equals to 15(y4)(y+4).
I am factoring polynomials, and trinomials using the GCF first, and then grouping. I can't find a video for this. Help please. Thanks!
im still confused
If you were to factor out the GCF that happened to be a term in the expression, would you completely eliminate it or leave it as 1?
why doesn't this video work?
IDK man, IDK man
I lost you at about 3:45, I don't understand the things after that.... __
What would the GCF of 12p^2 and 30q^5 be?
Grace,
12p^2 when factored to its primes is 2*2*3*p*p
30q^5 when factored to its primes is 2*3*5*q*q*q*q*q
The only common factors in both are 2*3.
So the Greatest Common Factor = 6
I hope that helps make it click for you.
12p^2 when factored to its primes is 2*2*3*p*p
30q^5 when factored to its primes is 2*3*5*q*q*q*q*q
The only common factors in both are 2*3.
So the Greatest Common Factor = 6
I hope that helps make it click for you.
when is the GCF of two or more numbers equal to one of the numbers?
How do I factor 25a^2 9b^2
How do you factor out 60x+20x^2+45?
OK, so you could factor out the 4x to the 3rd y using the first step, but then for the second step when Sal shows that you can take the remaining x and the 2 and put them in parenthesis, where did he get the plus sign from exactly? Is it because 2 is a positive factor and not a negative one?
I have to study for a math test tomorrow and I'm struggling with factoring things out. I also have to memorize sixteen different axioms and propertys. Any tips??
How do I find the sum of the numbers 56+64 as the product of their GCF and another sum
could you do the problem with just whole numbers please
What if one polynomial has a 5 in it and the other has a 10, lets say the question is "5ly + 10l*2 y*2. Can I write "5 times l times y and for the other one 5 time 2 times l times l times y times y? Like can I use different numbers?
I know its basic but it helped me to actually see the ones that are cross cancelled which I did in my notes so that when I did the division I could visualize; 4x^3y(1*x*1 + 2*1*1) since the original monomials have the terms adjacent to them so that they are basically; 4*x^4*y + 8*x^3*y. I think the comments below address this, but I wanted to post this for my own edification and in case it may help someone :)
Discuss the site
View general discussions about Khan Academy.
Flag inappropriate posts
Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians.
abuse
 disrespectful or offensive
 an advertisement
not helpful
 low quality
 not about the video topic
 contentious posts about politics, religion/atheism, or personal issues
 soliciting votes or seeking badges
 a homework question
 a duplicate answer
 repeatedly making the same post
wrong category
 a tip or thanks in Questions
 a question in Tips & Thanks
 an answer that should be its own question
about the site
 a question about Khan Academy
 a post about badges
 a technical problem with the site
 a request for features
Your SpinOffs
Your SpinOffs
Share a tip
Thank the author
Have something that's not a tip or thanks about this content?
This discussion area is not meant for answering homework questions.