Factor 7x^2-x-8

$7 x^{2} - x - 8$

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 $a \cdot c = 7 \cdot - 8 = - 56$ and whose sum is $b = - 1$ .

Factor $- 1$ out of $- x$ .

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

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

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

Apply the distributive property.

$7 x^{2} + 7 x - 8 x - 8$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$7 x (x + 1) - 8 (x + 1)$

Step 3

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

$(x + 1) (7 x - 8)$

Factor 7x^2-x-8

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