Factor 15x^3-9x^2-6x

$15 x^{3} - 9 x^{2} - 6 x$

Step 1

Factor $3 x$ out of $15 x^{3} - 9 x^{2} - 6 x$ .

Factor $3 x$ out of $15 x^{3}$ .

$3 x (5 x^{2}) - 9 x^{2} - 6 x$

Factor $3 x$ out of $- 9 x^{2}$ .

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

Factor $3 x$ out of $- 6 x$ .

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

Factor $3 x$ out of $3 x (5 x^{2}) + 3 x (- 3 x)$ .

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

Factor $3 x$ out of $3 x (5 x^{2} - 3 x) + 3 x (- 2)$ .

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

Step 2

Factor.

Factor by grouping.

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 $a \cdot c = 5 \cdot - 2 = - 10$ and whose sum is $b = - 3$ .

Factor $- 3$ out of $- 3 x$ .

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

Rewrite $- 3$ as $2$ plus $- 5$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$3 x (x (5 x + 2) - (5 x + 2))$

Factor the polynomial by factoring out the greatest common factor, $5 x + 2$ .

$3 x ((5 x + 2) (x - 1))$

Remove unnecessary parentheses.

$3 x (5 x + 2) (x - 1)$

Factor 15x^3-9x^2-6x

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