Precalculus Examples

$20 x^{3} - 8 x^{2} - 5 x + 2$

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.

$(20 x^{3} - 8 x^{2}) - 5 x + 2$

Step 1.2

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

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

Step 2

Factor the polynomial by factoring out the greatest common factor, $5 x - 2$ .

$(5 x - 2) (4 x^{2} - 1)$

Step 3

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

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

Step 4

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

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

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 $a = 2 x$ and $b = 1$ .

$(5 x - 2) ((2 x + 1) (2 x - 1))$

Step 5.2

Remove unnecessary parentheses.

$(5 x - 2) (2 x + 1) (2 x - 1)$