Trigonometry Examples

$3 b x^{3} + 2 b x^{2} - 12 b x - 8 b$

Step 1

Factor $b$ out of $3 b x^{3} + 2 b x^{2} - 12 b x - 8 b$ .

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Step 1.1

Factor $b$ out of $3 b x^{3}$ .

$b (3 x^{3}) + 2 b x^{2} - 12 b x - 8 b$

Step 1.2

Factor $b$ out of $2 b x^{2}$ .

$b (3 x^{3}) + b (2 x^{2}) - 12 b x - 8 b$

Step 1.3

Factor $b$ out of $- 12 b x$ .

$b (3 x^{3}) + b (2 x^{2}) + b (- 12 x) - 8 b$

Step 1.4

Factor $b$ out of $- 8 b$ .

$b (3 x^{3}) + b (2 x^{2}) + b (- 12 x) + b \cdot - 8$

Step 1.5

Factor $b$ out of $b (3 x^{3}) + b (2 x^{2})$ .

$b (3 x^{3} + 2 x^{2}) + b (- 12 x) + b \cdot - 8$

Step 1.6

Factor $b$ out of $b (3 x^{3} + 2 x^{2}) + b (- 12 x)$ .

$b (3 x^{3} + 2 x^{2} - 12 x) + b \cdot - 8$

Step 1.7

Factor $b$ out of $b (3 x^{3} + 2 x^{2} - 12 x) + b \cdot - 8$ .

$b (3 x^{3} + 2 x^{2} - 12 x - 8)$

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.

$b ((3 x^{3} + 2 x^{2}) - 12 x - 8)$

Step 2.2

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

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

Step 3

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

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

Step 4

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

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

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

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

Step 5.1.2

Remove unnecessary parentheses.

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

Step 5.2

Remove unnecessary parentheses.

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