In Exercises 69–78, factor each polynomial.x³ − 5 + 4x³y − 20y

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Hello, everyone. We are going to factor the following polynomial expression. Two H cubed minus four plus three H cubed K minus six K. Our answer choices are a parentheses H cubed plus two multiplied by the parentheses, two minus three K B, the parentheses H cubed plus two multiplied by the parentheses. Three K minus two C, the parentheses H cubed minus two multiplied by the parentheses. Three K plus two D. This polynomial is prime. I'm gonna go back to rewrite my original polynomial. So two H cubed minus four plus three H cubed K minus six K being that I have four terms. The first thing that I think of is that I should try to factor this by grouping. So I'm going to group the first two terms together in a set of parentheses. So two H cubed -4 is now in a set of parentheses. And I put a set of parentheses around three H cubed K - K. I recall that when I factor by grouping, I want to find a greatest common factor within each group to remove from the parentheses. So in the first set of parentheses, 2 h cubed -4. I know that the variable isn't going to be my greatest common factor. So I look at the two and the four and I know I could factor a two out of that. So I now have two multiplied by parentheses. H cubed minus two closed parentheses. Looking at my next group of parentheses, I have three H cubed K minus six K. I noticed I could take a three out of both terms. So that's gonna be part of my greatest common factor. I cannot take an H out of both terms, but I can take a K out of both terms. So my G C F there is three K. I'm gonna multiply it by parentheses and I'm gonna divide three H cubed K by three K leaving me with H cubed and minus or negative six K divided by three K will give me a negative two. So at this point in factorization, I have two multiplied by the parentheses. H cubed minus two plus three K multiplied by the parentheses H cubed minus two. I recognize that I have a binomial G C F of H cubed -2 as that is in both terms. So I'm gonna factor that out first write the parentheses H cubed minus two closed parentheses. And I'm gonna multiply that by another set of parentheses that has my coefficients in it. So two plus three K. So the values I factored out the first time are grouped together in my second parentheses. At this point, I have parentheses, each cubed minus two, multiplied by the parentheses two plus three K. And that looks like it should be my full factorization. Um The only difference between that and our answer choices is the addition is written in an opposite order. So what that means, addition can go in either order. Answer choice C is our answer choice and it is the parentheses H cubed minus two, multiplied by the parentheses. Three K plus two have a nice day.

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In Exercises 69–78, factor each polynomial.x³ − 5 + 4x³y − 20y

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