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.

x³ + 5x²

Accepted Answer

Welcome back. I am so glad you're here. We are asked to factor the following polynomial. The polynomial we're given is the to the third plus nine Z squared. Answer choice A says Z times parentheses, Z squared plus nine and parentheses answer choice B is nine, Z squared times parentheses, Z plus one and parentheses. Answer choice C is Z squared times parentheses, Z plus nine and parentheses, an answer choice D is nine Z times parentheses. Z plus one end parentheses. Well, we recall from previous lessons on factoring polynomial that we are going to compare our terms and we're specifically going to start by looking at the parts that are alike. Now, we notice that this first term here, the coefficient of Z cubed is one and if we compare one with nine, we won't be able to find the greatest common factor. They're both just divisible by one. So we can't factor out of one. And now the parts that are similar between both terms are the Z's. So we have Z to the third and Z squared. And we recall from previous lessons that when we are looking to factor out from variables, we look for the variable with the lowest degree. So between three and to the lowest degree is to, we're going to divide both variables by Z squared or in other words, we're able to factor out Z squared. And now that we know everything we're factoring out, we look at what will be left behind. So for the first one, we're taking Z to the third divided by Z squared, we recall from previous lessons that when we are dividing variables, we're going to subtract their exponents. So three minus 23 minus two is one. So we have Z to the first, which is just Z. So the first term, all that's left is Z. Now, for this second term plus nine Z squared, we couldn't take anything out of that nine, nothing was able to be factored out. So we need to be sure we bring that down plus nine. And now looking at Z squared divided by Z squared, Well, we're taking 2 -2, which is zero. So we have Z raised to the zero power and anything raised to the zero power is just one. So we're taking that nine times 19 times one is just nine. So we don't need to put the times one part, we can close this parentheses and this has now been factored. So we look at our answer choices for Z squared times parentheses, Z plus nine and parentheses. And that matches with answer choice C while done, we'll catch you on the next one.

In Exercises 1–22, factor the greatest common factor from each polynomial. x³ + 5x²

주요 개념

Greatest Common Factor (GCF)

Factoring Polynomials

Polynomial Terms

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