In Exercises 45–68, factor by grouping.x³− 3x² + 4x − 12

Question

Accepted Answer

Hello, today we're gonna be factoring the given polynomial. So what we are given is a polynomial of four terms. And whenever we want to factor a polynomial of four terms, the first thing we wanna do is try factoring by grouping, factoring by grouping allows us to group up the first two terms together and the last two terms of the polynomial together. And what we want to go ahead and do is go through each of the groups and factor out a common factor. So let's go ahead and take a look at the first group in the first group, we have a cubed minus two A squared. Now, between these two terms, there is at least two instances of A. So we can go ahead and factor out an A squared from the first group and factoring out an A squared from the first group allows us to rewrite it as a squared times the quantity A minus two. And now let's go ahead and repeat this process for the second group. In the second group, we have nine, a minus 18, both nine and 18 are multiples of nine. So we can go ahead and factor out a nine from the second group and factoring out a nine from the second group allows us to rewrite it as positive nine times the quantity A minus two. Now, after we factored out the common factors, notice that we have two instances of a minus two, we can go ahead and combine these two together by combining the leading coefficients together. And that's going to allow us to rewrite this as a squared plus nine times the quantity A minus two. And this is going to be the factor form of the given polynomial. And with that being said, the answer to this problem is going to be D. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 45–68, factor by grouping.x³− 3x² + 4x − 12

Key Concepts

Factoring by Grouping

Common Factors

Polynomial Expressions

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