Trigonometry Examples

$8 g^{3} + 10 g^{2} - 72 g - 90$

Step 1

Factor $2$ out of $8 g^{3} + 10 g^{2} - 72 g - 90$ .

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Step 1.1

Factor $2$ out of $8 g^{3}$ .

$2 (4 g^{3}) + 10 g^{2} - 72 g - 90$

Step 1.2

Factor $2$ out of $10 g^{2}$ .

$2 (4 g^{3}) + 2 (5 g^{2}) - 72 g - 90$

Step 1.3

Factor $2$ out of $- 72 g$ .

$2 (4 g^{3}) + 2 (5 g^{2}) + 2 (- 36 g) - 90$

Step 1.4

Factor $2$ out of $- 90$ .

$2 (4 g^{3}) + 2 (5 g^{2}) + 2 (- 36 g) + 2 (- 45)$

Step 1.5

Factor $2$ out of $2 (4 g^{3}) + 2 (5 g^{2})$ .

$2 (4 g^{3} + 5 g^{2}) + 2 (- 36 g) + 2 (- 45)$

Step 1.6

Factor $2$ out of $2 (4 g^{3} + 5 g^{2}) + 2 (- 36 g)$ .

$2 (4 g^{3} + 5 g^{2} - 36 g) + 2 (- 45)$

Step 1.7

Factor $2$ out of $2 (4 g^{3} + 5 g^{2} - 36 g) + 2 (- 45)$ .

$2 (4 g^{3} + 5 g^{2} - 36 g - 45)$

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.

$2 ((4 g^{3} + 5 g^{2}) - 36 g - 45)$

Step 2.2

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

$2 (g^{2} (4 g + 5) - 9 (4 g + 5))$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 g + 5$ .

$2 ((4 g + 5) (g^{2} - 9))$

Step 4

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

$2 ((4 g + 5) (g^{2} - 3^{2}))$

Step 5

Factor.

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Step 5.1

Factor.

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Step 5.1.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = g$ and $b = 3$ .

$2 ((4 g + 5) ((g + 3) (g - 3)))$

Step 5.1.2

Remove unnecessary parentheses.

$2 ((4 g + 5) (g + 3) (g - 3))$

Step 5.2

Remove unnecessary parentheses.

$2 (4 g + 5) (g + 3) (g - 3)$