Chapter 6: Q 54E (page 573)

In the following exercises, factor.
$x^{3} + x^{2} - x - 1$ .

Short Answer

Expert verified

The factors for the expression $x^{3} + x^{2} - x - 1$ are, $(x^{2} - 1) (x + 1)$ .

Step by step solution

Given expression is,

$x^{3} + x^{2} - x - 1$ .

The objective is, we need to find the factor for this expression.

First group each term with the common factors.

$x^{3} + x^{2} - x - 1 = (x^{3} + x^{2}) + (- x - 1)$

Now factor out the common factors.

$x^{3} + x^{2} - x - 1 = x^{2} (x + 1) - 1 (x + 1) = (x + 1) (x^{2} - 1)$

The obtained factors are, $(x + 1) (x^{2} - 1)$ .

Step 3 let us check the answer by multiplying the factors.

$(x^{2} - 1) (x + 1) = x^{3} + x^{2} - x - 1$

which is true.

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In the following exercises, factor.
$x^{3} + x^{2} - x - 1$ .

Short Answer

Step by step solution

Given expression is,

First group each term with the common factors.

Step 3 let us check the answer by multiplying the factors.

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In the following exercises, factor.x3+x2−x−1.

Short Answer

Step by step solution

Given expression is,

First group each term with the common factors.

Step 3 let us check the answer by multiplying the factors.

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, factor.
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