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## Algebra (all content)

### Course: Algebra (all content)>Unit 10

Lesson 12: Factoring polynomials by taking common factors

# Factoring polynomials: common factor (old)

An old video where Sal factors 4x⁴y+8x³y as 4x³y(x+2). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• 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!
• 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,
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
• I have to do this x4-x2 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^2-1). Factoring further it becomes x^2(x+1)(x-1). 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 y-variables 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(y-1). 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)(x-1)
• Shouldn't the title for this video be "How to factor a quadratic binomial"? Or is quartic a term I don't know? Genuinely asking. • At , why does he divide by 4x^3 y? • 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? • What is the difference between a binomial and a monomial? • So if I've been given y^2(2y - 1), 3(2y - 1) to find the GCF, is the GCF just (y^2 + 3), or do I have to do something more? Can I also get a link to the new version of this if there is one?   