Factor 4x^3-17x^2-15x

$4 x^{3} - 17 x^{2} - 15 x$

Step 1

Factor $x$ out of $4 x^{3} - 17 x^{2} - 15 x$ .

Factor $x$ out of $4 x^{3}$ .

$x (4 x^{2}) - 17 x^{2} - 15 x$

Factor $x$ out of $- 17 x^{2}$ .

$x (4 x^{2}) + x (- 17 x) - 15 x$

Factor $x$ out of $- 15 x$ .

$x (4 x^{2}) + x (- 17 x) + x \cdot - 15$

Factor $x$ out of $x (4 x^{2}) + x (- 17 x)$ .

$x (4 x^{2} - 17 x) + x \cdot - 15$

Factor $x$ out of $x (4 x^{2} - 17 x) + x \cdot - 15$ .

$x (4 x^{2} - 17 x - 15)$

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 $a \cdot c = 4 \cdot - 15 = - 60$ and whose sum is $b = - 17$ .

Factor $- 17$ out of $- 17 x$ .

$x (4 x^{2} - 17 (x) - 15)$

Rewrite $- 17$ as $3$ plus $- 20$

$x (4 x^{2} + (3 - 20) x - 15)$

Apply the distributive property.

$x (4 x^{2} + 3 x - 20 x - 15)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$x ((4 x^{2} + 3 x) - 20 x - 15)$

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

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

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

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

Remove unnecessary parentheses.

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

Factor 4x^3-17x^2-15x

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