Factor 7x^2+32x-15

$7 x^{2} + 32 x - 15$

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 $a \cdot c = 7 \cdot - 15 = - 105$ and whose sum is $b = 32$ .

Factor $32$ out of $32 x$ .

$7 x^{2} + 32 (x) - 15$

Rewrite $32$ as $- 3$ plus $35$

$7 x^{2} + (- 3 + 35) x - 15$

Apply the distributive property.

$7 x^{2} - 3 x + 35 x - 15$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(7 x^{2} - 3 x) + 35 x - 15$

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

$x (7 x - 3) + 5 (7 x - 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 x - 3$ .

$(7 x - 3) (x + 5)$

Factor 7x^2+32x-15

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