Factor 25x^3-55x^2-60x

$25 x^{3} - 55 x^{2} - 60 x$

Step 1

Factor $5 x$ out of $25 x^{3} - 55 x^{2} - 60 x$ .

Factor $5 x$ out of $25 x^{3}$ .

$5 x (5 x^{2}) - 55 x^{2} - 60 x$

Factor $5 x$ out of $- 55 x^{2}$ .

$5 x (5 x^{2}) + 5 x (- 11 x) - 60 x$

Factor $5 x$ out of $- 60 x$ .

$5 x (5 x^{2}) + 5 x (- 11 x) + 5 x (- 12)$

Factor $5 x$ out of $5 x (5 x^{2}) + 5 x (- 11 x)$ .

$5 x (5 x^{2} - 11 x) + 5 x (- 12)$

Factor $5 x$ out of $5 x (5 x^{2} - 11 x) + 5 x (- 12)$ .

$5 x (5 x^{2} - 11 x - 12)$

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 $a \cdot c = 5 \cdot - 12 = - 60$ and whose sum is $b = - 11$ .

Factor $- 11$ out of $- 11 x$ .

$5 x (5 x^{2} - 11 (x) - 12)$

Rewrite $- 11$ as $4$ plus $- 15$

$5 x (5 x^{2} + (4 - 15) x - 12)$

Apply the distributive property.

$5 x (5 x^{2} + 4 x - 15 x - 12)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$5 x ((5 x^{2} + 4 x) - 15 x - 12)$

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

$5 x (x (5 x + 4) - 3 (5 x + 4))$

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

$5 x ((5 x + 4) (x - 3))$

Remove unnecessary parentheses.

$5 x (5 x + 4) (x - 3)$

Factor 25x^3-55x^2-60x

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