In Exercises 1–22, factor the greatest common factor from each po...

Question

In Exercises 1–22, factor the greatest common factor from each polynomial.12xy − 6xz + 4xw

Accepted Answer

Welcome back. I am so glad you're here. We are asked to factor the following polynomial. We are given 20 A B minus 15 A C plus 10 A D. And our answer choices are answer choice A five A times parentheses B minus three C plus two D. Answer choice B is 58 times parentheses 20 minus three, C plus two D. Answer choice C is 58 times parentheses, four B minus three C plus two D and answer choice D is A times parentheses 20 B minus 15 C plus 10 A D. Alright. We recall from previous lessons that in order to factor a polynomial, we are going to look at the parts of each term that are alike. So let's start off with the coefficients. We look at 20 negative 15 and 10. And we ask ourselves, what is the greatest common factor that those three coefficients share? Is there anything that they can all be divided by? And if so what's the highest number they can all be divided by? And in this case, the highest number they can all be divided by is five. So that means we can factor out of five. Next, we see if they have any variables that are alike. And in this case, they all share an A so we can factor out. And A now the B and the C and the D are not alike. So we can't do any factoring with those. So we factored out five A. Now we just need to see what's left for each of our terms. So let's start with the 1st 1, 20 A B factoring out of five A or in other words, 20 A B divided by five A well, 20 divided by five. That is four. So there's four left from the 20 and A divided by A. Well, that's like taking a to the first divided by a to the first. And we recall from previous lessons that when we are dividing variables, we're going to subtract the exponents. So we're taking 1 -1 which is zero. So we have a to the zero and anything raised to the zero power equals one. So the A that's left, that's just one. Now, we could say four times one but four times one is just four. So we don't really need to say anything for that. A it's just been factored out and now we cannot forget to bring down this B term. Alright, the first term 20 A B has been factored. Now let's work on the second term. We take negative 15 divided by five, that's negative three. The A has been factored out that just leaves one and one times negative three is negative three. And now we can't forget to bring down this C. Let's work on the third term 10 divided by five. That is too. So we have plus two, the A is factored out and then we cannot forget to bring down this D and now we have done all of the factoring. So we want to look at our answer choices for five A times four B minus three C plus two D and that matches with answer choice. C well done. We'll catch you on the next one.

In Exercises 1–22, factor the greatest common factor from each polynomial.12xy − 6xz + 4xw

Key Concepts

Greatest Common Factor (GCF)

Factoring Polynomials

Polynomial Terms

Watch next