Trigonometry Examples

$8 x^{3} + 4 x^{2} - 18 x - 9$

Step 1

Factor out the greatest common factor from each group.

Tap for more steps...

Step 1.1

Group the first two terms and the last two terms.

$(8 x^{3} + 4 x^{2}) - 18 x - 9$

Step 1.2

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

$4 x^{2} (2 x + 1) - 9 (2 x + 1)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

$(2 x + 1) (4 x^{2} - 9)$

Step 3

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

$(2 x + 1) ({(2 x)}^{2} - 9)$

Step 4

Rewrite $9$ as $3^{2}$ .

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

Step 5

Factor.

Tap for more steps...

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 $b = 3$ .

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

Step 5.2

Remove unnecessary parentheses.

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