Pre-Algebra Examples

$(x^{3} + x^{2} - 9 x - 9) \div (x + 1)$

Step 1

Rewrite the division as a fraction.

$\frac{x^{3} + x^{2} - 9 x - 9}{x + 1}$

Step 2

Simplify the numerator.

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Step 2.1

Factor out the greatest common factor from each group.

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Step 2.1.1

Group the first two terms and the last two terms.

$\frac{(x^{3} + x^{2}) - 9 x - 9}{x + 1}$

Step 2.1.2

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

$\frac{x^{2} (x + 1) - 9 (x + 1)}{x + 1}$

Step 2.2

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

$\frac{(x + 1) (x^{2} - 9)}{x + 1}$

Step 2.3

Rewrite $9$ as $3^{2}$ .

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

Step 2.4

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 $b = 3$ .

$\frac{(x + 1) (x + 3) (x - 3)}{x + 1}$

Step 3

Cancel the common factor of $x + 1$ .

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Step 3.1

Cancel the common factor.

$\frac{(x + 1) (x + 3) (x - 3)}{x + 1}$

Step 3.2

Divide $(x + 3) (x - 3)$ by $1$ .

$(x + 3) (x - 3)$

Step 4

Expand $(x + 3) (x - 3)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$x (x - 3) + 3 (x - 3)$

Step 4.2

Apply the distributive property.

$x \cdot x + x \cdot - 3 + 3 (x - 3)$

Step 4.3

Apply the distributive property.

$x \cdot x + x \cdot - 3 + 3 x + 3 \cdot - 3$

Step 5

Combine the opposite terms in $x \cdot x + x \cdot - 3 + 3 x + 3 \cdot - 3$ .

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Step 5.1

Reorder the factors in the terms $x \cdot - 3$ and $3 x$ .

$x \cdot x - 3 x + 3 x + 3 \cdot - 3$

Step 5.2

Add $- 3 x$ and $3 x$ .

$x \cdot x + 0 + 3 \cdot - 3$

Step 5.3

Add $x \cdot x$ and $0$ .

$x \cdot x + 3 \cdot - 3$

Step 6

Simplify each term.

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Step 6.1

Multiply $x$ by $x$ .

$x^{2} + 3 \cdot - 3$

Step 6.2

Multiply $3$ by $- 3$ .

$x^{2} - 9$