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### Course: Algebra basics>Unit 7

Lesson 4: Factoring polynomials by 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 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.
• 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.
• how would you factor 4a^2+12ab+9b^2?
• If you take a closer look at the expression, you might be able to notice something. The first term, 4a^2, can be represented as (2a)^2. On the other hand, the third term, 9b^2, can be represented as (3b)^2. Rewriting the expression with these new representations, you would get (2a)^2+12ab+(3b)^2. Now if you look at it, you may be able to notice that it is a perfect square in the form of a^2+2ab+b^2, where "a" is 2a and "b" is 3b. This matches up, because a^2+2ab+b^2 = (2a)^2+2(2a)(3b)+(3b)^2 = 4a^2+12ab+9b^2. Knowing this, we can factor the expression in the form (a+b)^2 where "a" is 2a and b is 3b, so your final answer would be (2a+3b)^2.
(1 vote)
• 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.
• 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.
• what if there is no GCF
• That's ok. Many polynomials will not have a common factor. You will learn several factoring techniques to use when factoring polynomials. Your first step should always be to factor out the GCF if one exists.
• 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)