Algebra Examples

$2 x^{3} + 3 x^{2} - 2 x - 3$

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.

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

Step 1.2

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

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

Step 2

Factor the polynomial by factoring out the greatest common factor, $2 x + 3$ .

$(2 x + 3) (x^{2} - 1)$

Step 3

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

$(2 x + 3) (x^{2} - 1^{2})$

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 $b = 1$ .

$(2 x + 3) ((x + 1) (x - 1))$

Step 4.2

Remove unnecessary parentheses.

$(2 x + 3) (x + 1) (x - 1)$