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 $b = 1$ .

Multiply by $1$ .

$7 x^{2} + 1 x - 8$

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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