Factor 15x^2+8x-16

$15 x^{2} + 8 x - 16$

Step 1

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 $a \cdot c = 15 \cdot - 16 = - 240$ and whose sum is $b = 8$ .

Factor $8$ out of $8 x$ .

$15 x^{2} + 8 (x) - 16$

Rewrite $8$ as $- 12$ plus $20$

$15 x^{2} + (- 12 + 20) x - 16$

Apply the distributive property.

$15 x^{2} - 12 x + 20 x - 16$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(15 x^{2} - 12 x) + 20 x - 16$

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

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

Step 3

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

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

Factor 15x^2+8x-16

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