Factor 25x^2-30x-40

$25 x^{2} - 30 x - 40$

Step 1

Factor $5$ out of $25 x^{2} - 30 x - 40$ .

Factor $5$ out of $25 x^{2}$ .

$5 (5 x^{2}) - 30 x - 40$

Factor $5$ out of $- 30 x$ .

$5 (5 x^{2}) + 5 (- 6 x) - 40$

Factor $5$ out of $- 40$ .

$5 (5 x^{2}) + 5 (- 6 x) + 5 (- 8)$

Factor $5$ out of $5 (5 x^{2}) + 5 (- 6 x)$ .

$5 (5 x^{2} - 6 x) + 5 (- 8)$

Factor $5$ out of $5 (5 x^{2} - 6 x) + 5 (- 8)$ .

$5 (5 x^{2} - 6 x - 8)$

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 $a \cdot c = 5 \cdot - 8 = - 40$ and whose sum is $b = - 6$ .

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

$5 (5 x^{2} - 6 (x) - 8)$

Rewrite $- 6$ as $4$ plus $- 10$

$5 (5 x^{2} + (4 - 10) x - 8)$

Apply the distributive property.

$5 (5 x^{2} + 4 x - 10 x - 8)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$5 ((5 x^{2} + 4 x) - 10 x - 8)$

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

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

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

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

Remove unnecessary parentheses.

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

Factor 25x^2-30x-40

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