Algebra Examples

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

Step 1

Factor out the greatest common factor from each group.

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Step 1.1

Group the first two terms and the last two terms.

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

Step 1.2

Factor out the greatest common factor (GCF) from each group.

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

Step 2

Factor the polynomial by factoring out the greatest common factor, $x + 1$ .

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

Step 3

Rewrite $1$ as $1^{2}$ .

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

Step 4

Factor.

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Step 4.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$(x + 1) ((x + 1) (x - 1))$

Step 4.2

Remove unnecessary parentheses.

$(x + 1) (x + 1) (x - 1)$

Step 5

Combine exponents.

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Step 5.1

Raise $x + 1$ to the power of $1$ .

${(x + 1)}^{1} (x + 1) (x - 1)$

Step 5.2

Raise $x + 1$ to the power of $1$ .

${(x + 1)}^{1} {(x + 1)}^{1} (x - 1)$

Step 5.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(x + 1)}^{1 + 1} (x - 1)$

Step 5.4

Add $1$ and $1$ .

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