Precalculus Examples

$5 x^{3} + 10 x^{2} - 20 x - 40$

Step 1

Factor $5$ out of $5 x^{3} + 10 x^{2} - 20 x - 40$ .

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Step 1.1

Factor $5$ out of $5 x^{3}$ .

$5 (x^{3}) + 10 x^{2} - 20 x - 40$

Step 1.2

Factor $5$ out of $10 x^{2}$ .

$5 (x^{3}) + 5 (2 x^{2}) - 20 x - 40$

Step 1.3

Factor $5$ out of $- 20 x$ .

$5 (x^{3}) + 5 (2 x^{2}) + 5 (- 4 x) - 40$

Step 1.4

Factor $5$ out of $- 40$ .

$5 x^{3} + 5 (2 x^{2}) + 5 (- 4 x) + 5 \cdot - 8$

Step 1.5

Factor $5$ out of $5 x^{3} + 5 (2 x^{2})$ .

$5 (x^{3} + 2 x^{2}) + 5 (- 4 x) + 5 \cdot - 8$

Step 1.6

Factor $5$ out of $5 (x^{3} + 2 x^{2}) + 5 (- 4 x)$ .

$5 (x^{3} + 2 x^{2} - 4 x) + 5 \cdot - 8$

Step 1.7

Factor $5$ out of $5 (x^{3} + 2 x^{2} - 4 x) + 5 \cdot - 8$ .

$5 (x^{3} + 2 x^{2} - 4 x - 8)$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$5 ((x^{3} + 2 x^{2}) - 4 x - 8)$

Step 2.2

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

$5 (x^{2} (x + 2) - 4 (x + 2))$

Step 3

Factor the polynomial by factoring out the greatest common factor, $x + 2$ .

$5 ((x + 2) (x^{2} - 4))$

Step 4

Rewrite $4$ as $2^{2}$ .

$5 ((x + 2) (x^{2} - 2^{2}))$

Step 5

Factor.

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Step 5.1

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 $b = 2$ .

$5 ((x + 2) ((x + 2) (x - 2)))$

Step 5.2

Remove unnecessary parentheses.

$5 ((x + 2) (x + 2) (x - 2))$

Step 6

Factor.

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Step 6.1

Combine exponents.

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Step 6.1.1

Raise $x + 2$ to the power of $1$ .

$5 ({(x + 2)}^{1} (x + 2) (x - 2))$

Step 6.1.2

Raise $x + 2$ to the power of $1$ .

$5 ({(x + 2)}^{1} {(x + 2)}^{1} (x - 2))$

Step 6.1.3

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

$5 ({(x + 2)}^{1 + 1} (x - 2))$

Step 6.1.4

Add $1$ and $1$ .

$5 ({(x + 2)}^{2} (x - 2))$

Step 6.2

Remove unnecessary parentheses.

$5 {(x + 2)}^{2} (x - 2)$