# Transforming Factoring Into A Division Problem Video

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• 0:03 Factoring and Division
• 1:40 Dividing by your…
• 3:00 One More Example
• 4:25 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn how you can factor a problem by turning it into a division problem. Learn how this actually helps you to factor and keep your numbers straight.

## Factoring and Division

Yes, factoring and division actually are related to each other, and not only are they related to each other, they are also buddies, good friends that help each other out. Think of division as the buddy that gives you - factoring - his knee so that you can reach that super ripe peach at the top of the tree. This is what we'll be going over in this video lesson. I will show you how division will help you factor: how it will give you that extra boost that you need to reach that next level. This method works for polynomials where we can find a greatest common factor.

## Finding Your Greatest Common Factor

The first step in factoring is to find your greatest common factor. Recall that this is the number with or without variables that all the terms in your problem have in common. Let's try factoring the polynomial 10x + 5. First we compare the terms we have with each other: we have a '10x' and a '5.' Do they have anything in common? Yes they do! They each have a 5 in common.

Why a 5? Well, if we list out all the possible factors of each term, we will see that 5 is the highest value that they have in common. Since only the 10x has the x, we know that our greatest common factor won't have an x in it. So that leaves us with just the numbers.

So we are left with just comparing the factors of the numbers. So the factors of 10 are 1, 2, 5, and 10. The factors of 5 are 1 and 5. What is the highest number they have in common? It's the 5!

## Dividing By Your Greatest Common Factor

Now that we have our greatest common factor, we now turn our polynomial into fractions using that greatest common factor. We rewrite our problem as: 5(10x/5 + 5/5). See how the fractions are essentially division? This is where division, our buddy, steps in to give us a boost.

We've written a 5 outside of our polynomial-turned-fraction because we have to keep our problem the same. Since we are dividing each term by 5, we also need to multiply the whole problem by 5 to keep it the same. But to finish our problem, we only need to perform the division on the terms inside the parentheses. So, doing that, we get 5(2x + 1), and we are done factoring our problem!

We can check our work to see if it's correct by multiplying our answer out. So, 5(2x + 1) is equal to 5(2x) plus 5(1), which equals 10x + 5. Is this the same polynomial that we started with? Yes it is! So that means that my answer is correct.

Whenever you factor, it is a good idea to always perform this check to make sure you are doing your work correctly. I always recommend writing out everything you do so that you can tell what you are doing.

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