Problem 75 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

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

Step 1: Group the terms

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

Step 2: 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: \(x^{2}(x-1) + 2(x-1)\)

Step 3: 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: \((x-1)(x^{2}+2)\)