In Exercises 93–100, factor completely.

acx² − bcx − adx + bd

Question

In Exercises 93–100, factor completely.

acx² − bcx − adx + bd

Accepted Answer

Hello, today we're gonna be factoring the following polynomial completely. So what we are given is a polynomial of four terms. And whenever you have a polynomial of four terms, that's an indication that we should try factoring by grouping, factoring by grouping allows us to group up the first two terms together and the last two terms together. And what we want to go ahead and do is factor out a common factor from both of the groups. So let's take a look at the first group, we have M N Y squared minus P N Y. In both of the terms we have at least one N and in both of the terms we have at least one Y. That means that the greatest common factor of the first group is going to be N times Y. And now what about the second group? Well, in the second group, both of the terms have at least one Q in each of the terms. So the greatest common factor in the second group is going to be Q. So if we factor out these factors from both of the groups, what we are left with is N Y times the quantity M Y minus P plus Q times the quantity M Y minus P. And now notice that there are two instances of this quantity M Y minus P. We can go ahead and combine this into a single quantity by combining the coefficients together and by combining the coefficients together. What we are left with is N Y plus Q times the quantity M Y minus P. And this is going to be the completely factor version of the original polynomial. And with that being said, the answer to this problem is going to be B 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 93–100, factor completely. acx² − bcx − adx + bd

Key Concepts

Factoring Polynomials

Grouping Method

Common Factors

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