In Exercises 69–78, factor each polynomial.

ab − c − ac + b

Question

In Exercises 69–78, factor each polynomial.

ab − c − ac + b

Accepted Answer

Hello, today we're going to be factoring the following polynomial. So what we are given is a polynomial of four terms. And whenever we have a polynomial of four terms, that's a common sign that we should try factoring by grouping. So before we try the factory, let's go ahead and group up our like terms together. See the 1st and 4th term have a common factor of M and the 2nd and 3rd term have a common factor of N. So if we quickly reorder the terms in the given polynomial, we can go ahead and rewrite it as M K plus M minus N K minus N. And now in order to do factoring by grouping, we're gonna group up the first two terms and the last two terms together, and we're going to go through and factor out a common factor from each of the groups. So in the first group, the first term and second term have a common factor of M. So we can go ahead and factor out em from the first group. And that is going to leave us with M times the quantity K plus one. Next. In the second group, we have a common factor of N. So we can go ahead and factor out the end, but we want the first term to be positive. So we're going to factor out a negative end from the two terms in the second group. And that is going to leave us with minus N times the quantity K plus one. Now notice that we have two instances of the quantity K plus one, we could go ahead and combine these two together by adding the coefficients of the groups together. So adding the coefficients together is going to give us M minus N and that is going to allow us to combine the K plus ones into a single K plus one. And so the factored form of our given polynomial is going to be M minus N times K plus one. And with that being said, the answer to this problem is going to be a. 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 69–78, factor each polynomial. ab − c − ac + b

Key Concepts

Factoring Polynomials

Grouping Method

Greatest Common Factor (GCF)

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