Factor 3x^2-5x-8

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

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 $a \cdot c = 3 \cdot - 8 = - 24$ and whose sum is $b = - 5$ .

Factor $- 5$ out of $- 5 x$ .

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

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

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$3 x (x + 1) - 8 (x + 1)$

Step 3

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

$(x + 1) (3 x - 8)$

Factor 3x^2-5x-8

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