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Chapter 6: Problem 75

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

Short Answer

Expert verified
The factored form of the polynomial \(x^{3}-x^{2}+2x-2\) by the method of grouping is \((x-1)(x^{2}+2)\)

Step by step solution

01

Group the terms

Firstly, group the terms in pairs: \((x^{3}-x^{2}) + (2x-2)\)
02

Factor out common factors

The next step is to factor out common factors from each group. Here, from the first group we can fact out \(x^{2}\) and from the second group we can factor out 2. Doing that we obtain: \(x^{2}(x-1) + 2(x-1)\)
03

Factor by grouping

Now the polynomial is expressed as a product of two binomial expressions. We can now factor by grouping. Here because \(x-1\) is common in both terms, thus factoring it out we have: \((x-1)(x^{2}+2)\)

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Most popular questions from this chapter

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$x^{2}-3 x y-4 y^{2}$$

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$27 x^{2}+75$$

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Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$6 x^{2}+8 x y$$

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$12 y^{3}+16 y^{2}-3 y-4$$
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