Factor 15z^2-2z-8

$15 z^{2} - 2 z - 8$

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 $a \cdot c = 15 \cdot - 8 = - 120$ and whose sum is $b = - 2$ .

Factor $- 2$ out of $- 2 z$ .

$15 z^{2} - 2 (z) - 8$

Rewrite $- 2$ as $10$ plus $- 12$

$15 z^{2} + (10 - 12) z - 8$

Apply the distributive property.

$15 z^{2} + 10 z - 12 z - 8$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(15 z^{2} + 10 z) - 12 z - 8$

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

$5 z (3 z + 2) - 4 (3 z + 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 z + 2$ .

$(3 z + 2) (5 z - 4)$

Factor 15z^2-2z-8

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