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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 expression \(x^{3}-x^{2}+2 x-2\) by grouping is \((x-1)(x^{2}+2)\).

Step by step solution

01

Identify the Groups

First, identify the groups that have common factors. We can notice that \(x^{3}-x^{2}\) and \(2x-2\) can be grouped together because they both have common factors.
02

Factor Out the Common Factor from Each Group

Factor out \(x^{2}\) from the first group (\(x^{3}-x^{2}\)) to get \(x^{2}(x-1)\). Similarly, factor out \(2\) from the second group \(2x-2\) to get \(2(x-1)\). So now the expression \(x^{3}-x^{2}+2 x-2\) is equivalent to \(x^{2}(x-1) + 2(x-1)\).
03

Factor Out the Common Binomial

The expression \(x^{2}(x-1) + 2(x-1)\) can then be factored further by taking out the common binomial term \((x-1)\) which leads us to the factored form as \((x-1)(x^{2}+2)\)

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Most popular questions from this chapter

Use factoring to solve quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\)-intercepts. \((x-3)(x+8)=-30\)

Exercises \(150-152\) will help you prepare for the material covered in the next section. Factor: \((x-2)(x+3)-6\)

Use factoring to solve quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\)-intercepts. \((x+3)(3 x+5)=7\)

Each end of a glass prism is a triangle with a height that is 1 inch shorter than twice the base. If the area of the triangle is 60 square inches, how long are the base and height?

Make Sense? In Exercises \(115-118\), determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Although I can factor the difference of squares and perfect square trinomials using trial-and-error, recognizing these special forms shortens the process.
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