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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

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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.

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.

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 10*x* + 5. First we compare the terms we have with each other: we have a '10*x*' 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 10*x* 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!

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(10*x*/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(2*x* + 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(2*x* + 1) is equal to 5(2*x*) plus 5(1), which equals 10*x* + 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.

Let's look at another problem. This time, see if you can work the problem yourself and see if your work matches mine. Let's factor 14*x*^2 + 12*x*. First we look for our greatest common factor by comparing our terms, 14*x*^2 with 12*x*. Both have an *x*, so my common factor will have an *x*.

Now, the 14 and 12 have the number 2 in common. That's the highest number they have in common since we can't divide evenly by any of the higher numbers. So my greatest common factor is 2*x*.

Now we turn our problem into fractions by dividing everything by our greatest common factor. We use the 'slash,' the division symbol, to turn each term into a fraction. We realize that since we are dividing by 2*x*, we also need to multiply by 2*x* to keep our problem the same, so we rewrite our problem as 2*x*(14*x*^2/2*x* + 12*x*/2*x*).

We now perform the divisions inside the parentheses. We get 2*x*(7*x* + 6). We check our work by multiplying our answer out. We get 2*x* (7*x* + 6) = 14*x*^2 + 12*x*. Is this our original problem? Yes it is! So our final answer is 2*x*(7*x* + 6).

Now let's review what we've learned. We learned that to factor our greatest common factor, we can turn to division to help give us a boost. We first find our greatest common factor then we turn our problem into a division problem by dividing everything by our greatest common factor. In algebra, to keep our problem the same, if we divide by a certain number, we also need to multiply by that term, so we also multiply by our greatest common factor.

Next, we leave our multiplication alone and just perform the division on each term. This will leave us with the factored form, or answer. To check our answer, we perform the multiplication to see if we get our original problem. If we do, then we are done, and our factored form is our answer.

Once you have completed this lesson, you should be able to use division to find the greatest common factor for a polynomial.

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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

- What is Factoring in Algebra? - Definition & Example 5:32
- How to Find the Prime Factorization of a Number 5:36
- Using Prime Factorizations to Find the Least Common Multiples 7:28
- Equivalent Expressions and Fraction Notation 5:46
- Using Fraction Notation: Addition, Subtraction, Multiplication & Division 6:12
- Factoring Out Variables: Instructions & Examples 6:46
- Combining Numbers and Variables When Factoring 6:35
- Transforming Factoring Into A Division Problem 5:11
- Go to High School Algebra: Factoring

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