Factor out the greatest common factor from each polynomial. See E...

Question

Factor out the greatest common factor from each polynomial. See Example 1. -4p^3q^4-2p^2q^5

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression 32 A to the fourth B to the third plus eight A to the third B to the seventh and we are asked to factor it. So what does that mean? We recall from previous lessons? We're going to look at each of these two things being added together and we are going to compare them and ask ourselves, is there anything we can factor out even more specifically, we are going to compare the things that are alike. So we're going to look at the whole numbers. We're going to look at the A terms and we're going to look at the B terms and for each of those comparisons, we'll ask, is there any factor that they have in common that we can factor out? So let's do our first comparison. That's 32 and eight. Did they share any factors that we can factor out? Yes, they're both divisible by 88 is the greatest common factor. So we can factor out an eight. Now, let's look at our A s we have A to the fourth and A to the third. Well, when we have variables with exponents, we are going to look at the degrees of those exponents and we are going to find the one with the lowest degree. In this case, that is to the third, A to the third. And we're going to divide both of these by A to the third because A to the third will come out of both. So that means we can factor out in front and A to the third. Now, let's look at our BS, we have B to the third and B to the seventh. Same deal with these, we look at the degrees of the variables exponents and we find the lowest one and that is in this case, B to the third, B to the third is lower than B to the seventh. So we factor out A B to the third. Great. Well, we're dividing by A, A to the third, B to the third. So what's left? Now, we do that division that we set up on the right hand side, we take 32 divided by the eight that we factored out 32 divided by eight is four. So there's a four remaining there. We take A to the fourth divided by A to the third. We recall that when we are dividing variables with exponents, we are going to subtract those exponents. So this is four minus three that equals one. So this is A to the first or just A. So we've now got a left from that first section and now we've got B to the third divided by B to the third and that equals one. We do not need to put that one because we have the four times the A there and that times one is just four A. All right. Now, let's do this second section. We'll take the eight divided by eight that we factored out and eight divided by eight is one. Well, we might need to put a one down there if all of these are ones, but if not, it'll just be one times whatever we find. So let's do the next one. The A's eight of the third divided by eight to the third. That again is one B to the seventh divided by B to the third. Ah, there we go seven minus three for the exponents will give us A B to the fourth. So it's B to the fourth times, one times one, which is just plus B to the fourth. All right, we have factored out our eight A to the third B to the third and we look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

Factor out the greatest common factor from each polynomial. See Example 1. -4p^3q^4-2p^2q^5

Key Concepts

Greatest Common Factor (GCF)

Factoring Polynomials

Polynomial Terms

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