Factor -10x^3+5x^2+140x

$- 10 x^{3} + 5 x^{2} + 140 x$

Step 1

Factor $- 5 x$ out of $- 10 x^{3} + 5 x^{2} + 140 x$ .

Factor $- 5 x$ out of $- 10 x^{3}$ .

$- 5 x (2 x^{2}) + 5 x^{2} + 140 x$

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

$- 5 x (2 x^{2}) - 5 x (- x) + 140 x$

Factor $- 5 x$ out of $140 x$ .

$- 5 x (2 x^{2}) - 5 x (- x) - 5 x (- 28)$

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

$- 5 x (2 x^{2} - x) - 5 x (- 28)$

Factor $- 5 x$ out of $- 5 x (2 x^{2} - x) - 5 x (- 28)$ .

$- 5 x (2 x^{2} - x - 28)$

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 $a \cdot c = 2 \cdot - 28 = - 56$ and whose sum is $b = - 1$ .

Factor $- 1$ out of $- x$ .

$- 5 x (2 x^{2} - (x) - 28)$

Rewrite $- 1$ as $7$ plus $- 8$

$- 5 x (2 x^{2} + (7 - 8) x - 28)$

Apply the distributive property.

$- 5 x (2 x^{2} + 7 x - 8 x - 28)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$- 5 x ((2 x^{2} + 7 x) - 8 x - 28)$

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

$- 5 x (x (2 x + 7) - 4 (2 x + 7))$

Factor the polynomial by factoring out the greatest common factor, $2 x + 7$ .

$- 5 x ((2 x + 7) (x - 4))$

Remove unnecessary parentheses.

$- 5 x (2 x + 7) (x - 4)$

Factor -10x^3+5x^2+140x

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