In Exercises 1–22, factor the greatest common factor from each po...

Question

In Exercises 1–22, factor the greatest common factor from each polynomial.30x²y³ − 10xy²

Accepted Answer

Welcome back. I am so glad you're here. We are asked to factor the following polynomial. The polynomial we are given is 28 A squared B to the third minus seven A B squared. And our answer choices are answer choice A seven A B squared times parentheses for A B minus one and parentheses, answer choice B is A B squared times parentheses for A B minus one. And parentheses answer choice C is seven A B squared times parentheses A B minus one and parentheses, an answer choice D is seven A B squared times parentheses for A B minus seven and parentheses. While we recall from previous lessons that the first step in factoring polynomial is to look at the terms and look at the parts that are alike. So we'll start with the coefficients. So the first term's coefficient is 28 and the second term's coefficient is negative seven. And we ask ourselves, what is the greatest common factor between those two coefficients and between 28 negative seven? The greatest common factor is seven. So we can factor out a seven. The next part of each of the two terms that's alike are the A's, the first term has an A squared, the second term has an A and that's the same as a to the first. And we recall from previous lessons when we have variables, when we are looking at what to factor out, we want to find the degree that is the lowest for the variables. So we have a degree of two and a degree of one, the lowest degree is one. So we're going to factor out or divide both by A to the first or just a. Alright, next, we look at these bees, they both have bees so we can factor out some bees. The first term has B to the third. The second term has B squared. The lowest degree between three and two is two. So we can divide both or factor out A B squared. So now we figured out what to factor out, we just need to figure out what's left behind. So we are going to do that division that we have set up taking A squared B to the third divided by seven A B squared starting with the coefficients 28 divided by seven is four. So there's a four left for the first term inside the parentheses. A square divided by A to the first. We recall from previous lessons that when we are dividing variables, we are going to subtract their exponents. So we take 2 -1, 2 -1 is one. So we have eight of the first, which is just a and now we have B to the third divided by B squared. Well, three minus two is one. So we have B to the first which is just be, and of the first term, all that's left is for A B. Now let's work on the second term we're taking negative seven divided by seven that leaves us with negative one. So we put minus one A to the first divided by A, to the first subtracting those exponents, one minus one is zero. We have A to the zero. Well, anything to the zero power is equal to one. So we're taking negative one times one, negative, one times one is just negative one. So because that negative one is there, we don't need to put another one to multiply by that negative one lastly B squared divided by B squared. Well, two minus two is zero. So we have B to the zero, which is one. Now we can close that parentheses and we have this polynomial fully factored. Now we look at our answer choices for seven A B squared times parentheses for A B minus one. And that matches with answer choice. A well done. We'll catch you on the next one.

In Exercises 1–22, factor the greatest common factor from each polynomial.30x²y³ − 10xy²

Key Concepts

Greatest Common Factor (GCF)

Factoring Polynomials

Polynomial Terms

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