Precalculus Examples

$3 x^{3} - 4 x^{2} - 12 x + 16$

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.

$(3 x^{3} - 4 x^{2}) - 12 x + 16$

Step 1.2

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

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

Step 2

Factor the polynomial by factoring out the greatest common factor, $3 x - 4$ .

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

Step 3

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

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

Step 4

Factor.

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Step 4.1

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 $b = 2$ .

$(3 x - 4) ((x + 2) (x - 2))$

Step 4.2

Remove unnecessary parentheses.

$(3 x - 4) (x + 2) (x - 2)$