Precalculus Examples

$f (x) = 2 x^{3} - 4 x^{2} - 10 x + 20$

Step 1

Factor $2$ out of $2 x^{3} - 4 x^{2} - 10 x + 20$ .

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Step 1.1

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

$f (x) = 2 (x^{3}) - 4 x^{2} - 10 x + 20$

Step 1.2

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

$f (x) = 2 (x^{3}) + 2 (- 2 x^{2}) - 10 x + 20$

Step 1.3

Factor $2$ out of $- 10 x$ .

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

Step 1.4

Factor $2$ out of $20$ .

$f (x) = 2 x^{3} + 2 (- 2 x^{2}) + 2 (- 5 x) + 2 \cdot 10$

Step 1.5

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

$f (x) = 2 (x^{3} - 2 x^{2}) + 2 (- 5 x) + 2 \cdot 10$

Step 1.6

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

$f (x) = 2 (x^{3} - 2 x^{2} - 5 x) + 2 \cdot 10$

Step 1.7

Factor $2$ out of $2 (x^{3} - 2 x^{2} - 5 x) + 2 \cdot 10$ .

$f (x) = 2 (x^{3} - 2 x^{2} - 5 x + 10)$

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.

$f (x) = 2 ((x^{3} - 2 x^{2}) - 5 x + 10)$

Step 2.2

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

$f (x) = 2 (x^{2} (x - 2) - 5 (x - 2))$

Step 3

Factor.

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Step 3.1

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

$f (x) = 2 ((x - 2) (x^{2} - 5))$

Step 3.2

Remove unnecessary parentheses.

$f (x) = 2 (x - 2) (x^{2} - 5)$