Trigonometry Examples

$12 x^{3} - 15 x^{2} - 18 x$

Step 1

Factor out the GCF of $3 x$ from $12 x^{3} - 15 x^{2} - 18 x$ .

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Step 1.1

Factor out the GCF of $3 x$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $3 x$ from the expression $12 x^{3}$ .

$3 x (4 x^{2}) - 15 x^{2} - 18 x$

Step 1.1.2

Factor out the GCF of $3 x$ from the expression $- 15 x^{2}$ .

$3 x (4 x^{2}) + 3 x (- 5 x) - 18 x$

Step 1.1.3

Factor out the GCF of $3 x$ from the expression $- 18 x$ .

$3 x (4 x^{2}) + 3 x (- 5 x) + 3 x (- 6)$

Step 1.2

Since all the terms share a common factor of $3 x$ , it can be factored out of each term.

$3 x (4 x^{2} - 5 x - 6)$

Step 2

Factor by grouping.

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Step 2.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 4 \cdot - 6 = - 24$ and whose sum is $b = - 5$ .

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Step 2.1.1

Factor $- 5$ out of $- 5 x$ .

$3 x (4 x^{2} - 5 x - 6)$

Step 2.1.2

Rewrite $- 5$ as $3$ plus $- 8$

$3 x (4 x^{2} + (3 - 8) x - 6)$

Step 2.1.3

Apply the distributive property.

$3 x (4 x^{2} + 3 x - 8 x - 6)$

Step 2.2

Factor out the greatest common factor from each group.

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Step 2.2.1

Group the first two terms and the last two terms.

$3 x ((4 x^{2} + 3 x) - 8 x - 6)$

Step 2.2.2

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

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

Step 2.3

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

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