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.4x²y³ + 6xy

Accepted Answer

Welcome back. I am so glad you're here. We are asked to factor the following polynomial were given eight P squared Q to the third plus 18 P Q. And our answer choices are answer choice A two PQ times parentheses, four PQ squared plus nine and parentheses. Answer choice B two times parentheses, four PQ squared plus nine PQ and parentheses and choice C two PQ times parentheses, four PQ squared plus nine Q and parentheses and answer choice D two PQ times parentheses, four PQ squared plus nine P and parentheses. So we recall from previous lessons that when factoring a polynomial is, we're going to look at the parts of each polynomial that are similar. So let's start off looking at the coefficients we have eight and 18. And we want to ask ourselves what's the greatest common factor between those two coefficients and eight and 18 are both divisible by two. So we can factor out a two. The next part of the two terms that are alike are these peas? The first term has A P squared. The second term has A P P is the same as P two. The first we recall from previous lessons that when we are going to factor variables, we look for the variable with the lowest degree. So the variable with the lowest degree between two and one is one. Now we're going to factor out A P to the first or just A P. And then the last part that they both share is this Q part. So the first term has Q to the third and the second term has just Q, which is Q to the first. And again, looking for the term with the lowest degree Q two, the first is lower than Q to the third. So we will be dividing both terms by Q two the first or factoring out a cue. Now we know what can be factored out. We need to see what is left behind when we do that factoring. So we're going to do the division. We have set up, we have eight P squared Q to the third divided by two P Q. So let's start off with the coefficients eight divided by two, is four. So there's a four left from the first term and that goes inside the parentheses P squared divided by P to the first, we recall from previous lessons that when we're dividing variables, we are going to subtract the exponents. So two minus one and two minus one equals one. So we're left with P to the first which is just P. Now the last part of the first term Q to the third divided by Q two. The first, well, three minus one equals two. So we have Q squared left now working on the second term 18 P Q divided by two PQ well, 18 divided by two that leaves us with nine. So we have a plus nine P to the first divided by P to the first one minus one is zero. So we have P to the zero. Well, anything raised to the zero, power equals one. So we're taking that nine times one. Well, nine times one is nine. We don't need to put the times one because that nine is already there. The last part two, the first divided bike to the first one minus one is zero. So we have Q to the zero, which is just one. And again, we don't need to put that so we can close this parentheses. And now we have fully factored this polynomial. And next, we want to look at our answer choices, 42 PQ times parentheses, four PQ squared plus nine. And that matches with answer choice a while done. We'll catch you on the next one.

In Exercises 1–22, factor the greatest common factor from each polynomial.4x²y³ + 6xy

Key Concepts

Greatest Common Factor (GCF)

Factoring Polynomials

Polynomial Terms

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