Factor 7x^2-16x-15

$7 x^{2} - 16 x - 15$

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 $b = - 16$ .

Factor $- 16$ out of $- 16 x$ .

$7 x^{2} - 16 (x) - 15$

Rewrite $- 16$ as $5$ plus $- 21$

$7 x^{2} + (5 - 21) x - 15$

Apply the distributive property.

$7 x^{2} + 5 x - 21 x - 15$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(7 x^{2} + 5 x) - 21 x - 15$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 x + 5$ .

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

Factor 7x^2-16x-15

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