Precalculus Examples

$2 x^{3} - 4 x^{2} - 8 x + 16$

Step 1

Factor $2$ out of $2 x^{3} - 4 x^{2} - 8 x + 16$ .

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Step 1.1

Factor $2$ out of $2 x^{3}$ .

$2 (x^{3}) - 4 x^{2} - 8 x + 16$

Step 1.2

Factor $2$ out of $- 4 x^{2}$ .

$2 (x^{3}) + 2 (- 2 x^{2}) - 8 x + 16$

Step 1.3

Factor $2$ out of $- 8 x$ .

$2 (x^{3}) + 2 (- 2 x^{2}) + 2 (- 4 x) + 16$

Step 1.4

Factor $2$ out of $16$ .

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

Step 1.5

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

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

Step 1.6

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

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

Step 1.7

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

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

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.

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

Step 2.2

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

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

Step 3

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

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

Step 4

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

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

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 $b = 2$ .

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

Step 5.2

Remove unnecessary parentheses.

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

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 $1$ .

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

Step 6.1.2

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

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

Step 6.1.3

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

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

Step 6.1.4

Add $1$ and $1$ .

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

Step 6.2

Remove unnecessary parentheses.

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