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Chapter 0: Problem 12

Factor by grouping. $$x^{3}-3 x^{2}+4 x-12$$

Short Answer

Expert verified
The factored form of the given polynomial is \((x^{2}+4)(x-3).\)

Step by step solution

01

Separate the polynomial into two groups

To factor by grouping, first group the terms two by two, like this: \( (x^{3}-3 x^{2}) + (4 x-12) \). Note that we keep the signs within parentheses.
02

Factor out any common factors in each group

The next step is to factor out the largest common factor from each group separately. In the first group, we can factor out \(x^{2}\) to get: \(x^{2}(x-3) \). In the second group, we can factor out 4, yielding: \(4(x-3)\). This gives us: \(x^{2}(x-3) + 4(x-3)\).
03

Factor out the common binomial

In the previous step, we see that both groups share the common binomial \(x-3\). We can treat this entire binomial as a common factor. We thus factor out \( (x-3)\) to get: \((x^{2}+4)(x-3)\).

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Most popular questions from this chapter

What does \(a^{\frac{m}{n}}\) mean?

Insert either < or > in the shaded area between the numbers to make the statement true. $$-\pi \quad-3.5$$

will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x^{2},\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with \(-3\) and ending with 3 .

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