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## Algebra 2

### Course: Algebra 2>Unit 3

Lesson 3: Taking common factors

# Taking common factor from trinomial

Break down the process of taking common factors from trinomials. Learn how to identify the greatest common factor of a trinomial expression and use it to simplify the expression. Follow along as Sal factors 4x⁴y-8x³y-2x² as 2x²(2x²y-4xy-1) by taking the greatest common factor. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• At ... I know this is right, I just need an explanation.

How does x^2 go into x^3 and x^4?
• 5 goes into 15, 3 times (5*3=15)
8 goes into 16, 2 times (8*2=16)
9 goes into 54, 6 times(9*6=54)
x^2 goes into x^3, x times (x^2 * x=x^3)
x^2 goes into x^4, x^2 times (x^2 * x^2 = x^4)
• why did sal multiply and divide 2x squared?
• It may not be the best way to describe/ think about it. Do you understand how 4x^4y can be rewritten as (2x^2)(2x^2y)? It's basically that thinking, and then using the method of (5x^2+4xy+6x) = x(5x+4y+6) If you don't get that relation try working n reverse and distribute the x. Factoring a lot of times can be thought of as reverse distributing. Does that help?
• why we have taken only smallest no.
• I'm assuming you meant the smallest number--we take the smallest number out of 2 , 4, and 8 because 2 is the largest number that can divide EACH of the numbers evenly. If we wanted to use 2, 4, or 8--or any number, really--we could, but it would make it more complicated because we would have fractions.
• how would you factor 4a^2+12ab+9b^2?
• I tried to do this for a question, and Khan Academy said I was incorrect, any tips?
(3b^5)+(15b^4)-(18b^7) = 3(b^5 + 5^4 - 6b^7)
• First, you lost the variable in the middle term of your answer.
Next, you need to factor out the greatest common factor. You found the numeric portion, however, you didn't look at the variables. The greatest common factor must include some number of b's because all the terms have b's.
Give it a try. If you still can't get the right answer, comment back.
• I commonly see in posts and comments, below, this symbol --that I've inclosed within quotation marks, " ^ ". It usually comes after a letter and before a number. Is this symbol used to express an exponent?
• yes, it is hard to write an exponent on a computer so the use the "^" symbol and then the number.
• Wait, x cubed is divisible by x squared? I'm confused.
• Yes, x^3 is divisible by x^2.
x^3 = x*x*x and x^2 = x*x
They share a common factor os x^2. If you did that out your are left with x. This is just like if you have 8/4. 8 is 2^3 and 4=2^2. When you divide 8 by 4 you get 2.

Hope this helps.
• How would we factor x^2+4x+3 then?
• How do you factor 8k^2 - 16k + 6
• Using x, start with seeing all even numbers, so factor out a 2 to get 2(4x^2-8x+3). One way is to multiply ac to get 12 (slide the 4 which will later be used for dividing) and factor the related equation of 2(x^2-8x+12)=2(x-6)(x-2). To finish slide the 4 back by dividing and reduce to get 2(x-6/4)(x-2/4)=2(x-3/2)(x-1/2) then the denominators go to the front to end up with 2(2x-3)(2x-1)
So another example would be 10x^2 - x - 2.
Multiply ac and move to get x^2 - x - 20
Factor (x-5)(x+4), divide by 10 (x-5/10)(x-4/10)
reduce (x-1/2)(x+2/5) and move denominator (2x-1)(5x+2)
• I understand pretty much all of this, but just so I know:
at , why is y/2x² y? I understand with 8x³y/2x² 8/2 is 4, and x³ cancels out the x² in the denominator, but why is y/2 y?