Factor 16x^2-56x-32

$16 x^{2} - 56 x - 32$

Step 1

Factor $8$ out of $16 x^{2} - 56 x - 32$ .

Factor $8$ out of $16 x^{2}$ .

$8 (2 x^{2}) - 56 x - 32$

Factor $8$ out of $- 56 x$ .

$8 (2 x^{2}) + 8 (- 7 x) - 32$

Factor $8$ out of $- 32$ .

$8 (2 x^{2}) + 8 (- 7 x) + 8 (- 4)$

Factor $8$ out of $8 (2 x^{2}) + 8 (- 7 x)$ .

$8 (2 x^{2} - 7 x) + 8 (- 4)$

Factor $8$ out of $8 (2 x^{2} - 7 x) + 8 (- 4)$ .

$8 (2 x^{2} - 7 x - 4)$

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 $a \cdot c = 2 \cdot - 4 = - 8$ and whose sum is $b = - 7$ .

Factor $- 7$ out of $- 7 x$ .

$8 (2 x^{2} - 7 (x) - 4)$

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

$8 (2 x^{2} + (1 - 8) x - 4)$

Apply the distributive property.

$8 (2 x^{2} + 1 x - 8 x - 4)$

Multiply $x$ by $1$ .

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$8 (x (2 x + 1) - 4 (2 x + 1))$

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

$8 ((2 x + 1) (x - 4))$

Remove unnecessary parentheses.

$8 (2 x + 1) (x - 4)$

Factor 16x^2-56x-32

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