Factor 5x^2-6x-8

$5 x^{2} - 6 x - 8$

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 $a \cdot c = 5 \cdot - 8 = - 40$ and whose sum is $b = - 6$ .

Factor $- 6$ out of $- 6 x$ .

$5 x^{2} - 6 (x) - 8$

Rewrite $- 6$ as $4$ plus $- 10$

$5 x^{2} + (4 - 10) x - 8$

Apply the distributive property.

$5 x^{2} + 4 x - 10 x - 8$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} + 4 x) - 10 x - 8$

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

$x (5 x + 4) - 2 (5 x + 4)$

Step 3

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

$(5 x + 4) (x - 2)$

Factor 5x^2-6x-8

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