In Exercises 11–16, factor by grouping. x^3+6x^2−2x−12

Question

Accepted Answer

Hello today we're going to be factoring a polynomial. So the polynomial given to us is X cubed plus six, X squared minus eight, X minus 48. So notice how this polynomial has four terms with it. Since this polynomial has four terms. We can go ahead and factor by grouping and factor by grouping states that we go ahead and group up the first two terms together and the last two terms. And we want to go ahead and identify a greatest common factor in both of these groups to factor out. Well, if we take a look at our first group, the terms given to us are x cubed and six X squared. Both of these terms have the common factor of X squared. So the greatest common factor for our first group is going to be X squared. Now for our second group we have negative eight. X and negative 48 8 and 48 have the common factor of eight. However, we want to go ahead and factor out a quantity that allows this first term to be positive inside the group. So this group is going to have the greatest common factor of negative eight. So if we factor out the greatest common factors, the first group is going to give us x squared times the quantity X plus six. And if we factor out negative eight from the second group we get negative eight times the quantity X plus six. Now both of these quantities have the common term X-plus six. So we can combine both of these into a single factor and in order to do that we can go ahead and just add the leading coefficients together. Doing so is going to give us x squared minus eight times the quantity X plus six, X squared minus eight is not factory bubble. So this is going to be the fully factored version of our given polynomial. And that means that the answer to this problem is going to be a. So I hope this video helps you in understanding how to factor by grouping and I'll go ahead and see you all in the next video.

In Exercises 11–16, factor by grouping. x^3+6x^2−2x−12

Key Concepts

Factoring by Grouping

Common Factors

Polynomial Degree

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