Factor 5x^2+3x-8

$5 x^{2} + 3 x - 8$

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 $b = 3$ .

Factor $3$ out of $3 x$ .

$5 x^{2} + 3 (x) - 8$

Rewrite $3$ as $- 5$ plus $8$

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$5 x (x - 1) + 8 (x - 1)$

Step 3

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

$(x - 1) (5 x + 8)$

Factor 5x^2+3x-8

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