In Exercises 16–17, factor completely.

xy − 6x + 2y − 12

Question

In Exercises 16–17, factor completely.

xy − 6x + 2y − 12

Accepted Answer

Hello, today we're gonna be factoring the given expression. So what we are given is X Y minus nine X plus 11, Y minus 99. Now, what we have here is a polynomial of four terms. And whenever we have a polynomial of four terms, we can go ahead and factor this using factoring by grouping. So what we're going to do is we're going to group up the first two terms together and we're going to group up the last two terms together and we're gonna go through each group and factor out a greatest common factor. So looking at the first group, we have X Y minus nine X, each term here has at least one X. So we can go ahead and factor out an X from the first group. And in the second group, we have 11, Y minus 99 11 and 99 share a common multiple of 11. So we can go ahead and factor out an 11 from the second group. So if we factor out these values from the two groups, we can rewrite the expression as X times the quantity Y minus nine plus 11 times the quantity Y minus nine. And now notice that we have two instances of the value Y -9, we can go ahead and combine these into a single Y -9 by adding the coefficients together. So if we add the coefficients together, what we can do is rewrite the expression as X plus times the quantity Y minus nine. And this is going to be the completely factored version of the given expression. And with that being said, the answer to this problem is going to be D. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 16–17, factor completely. xy − 6x + 2y − 12

Key Concepts

Factoring Polynomials

Grouping Method

Common Factors

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