Factor by any method. See Examples 1–7. x^2+xy-5x-5y

Question

Accepted Answer

Hey everyone here we are asked to factor the following polynomial where we have x squared minus two X. Y plus four X minus eight Y. Now, our first step in factoring this expression here is to find the greatest common factor of our first two terms. As well as finding the greatest common factor of our last two terms. So starting with our first set of terms, we again are finding the greatest common factor of X squared and negative two. Xy Well, the greatest common factor here is just X. And now for our last two terms, again finding the greatest common factor of four X and negative eight. Y. Well, the greatest common factor between these two terms is just four. So now again we need to factor out these greatest common factors from both sets of terms. And so we need to rewrite our expression here and we have X. The first greatest common factor times the quantity of x minus two, Y plus. Our second greatest common factor was four. So we have four times the quantity of x minus two Y. And now looking at our rewritten expression, we see that we have a common term in both of our terms here, which is this expression? This quantity of x minus two Y. So since we have a common term here we can go ahead and factor that out. But when we factor it out, we are left with just X and plus four. So rewriting our expression using this information, we have the quantity of x minus two, Y. And again that leaves us with just X plus four. So we have the quantity of X minus two Y times the quantity of X plus four. And there aren't any other terms which we can factor out from either sets of parentheses here. So this is our final factored form of our original expression, which leaves us with answer choice. C. Thanks for watching. I hope you found this video helpful, and I'll see you again next time.

Factor by any method. See Examples 1–7. x^2+xy-5x-5y

Key Concepts

Factoring Polynomials

Grouping Method

Common Factors

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