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Chapter 0: Problem 14

Factor by grouping. $$x^{3}+6 x^{2}-2 x-12$$

Short Answer

Expert verified
The factorized form of the expression \(x^{3}+6 x^{2}-2 x-12\) by grouping is \((x^{2}-2)(x+6)\).

Step by step solution

01

Group the Terms

Divide the given expression into two groups. The given expression is \(x^{3}+6 x^{2}-2 x-12\). It can be written as \((x^{3}+6 x^{2})+(-2 x-12)\).
02

Factor Each Group

Find the common factors of each group and factorize them. The first group \(x^{3}+6 x^{2}\) can be factorized as \(x^{2}(x+6)\). The second group \(-2 x-12\) can be factorized as \(-2(x+6)\).
03

Combine Like Terms

Combine the like terms of the factored groups. Thus the expression becomes \((x^{2}-2)(x+6)\).

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Most popular questions from this chapter

This will help you prepare for the material covered in the next section. If 6 is substituted for \(x\) in the equation $$2(x-3)-17=13-3(x+2)$$ is the resulting statement true or false?

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