Factor 3z^2+8z-16

$3 z^{2} + 8 z - 16$

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 $a \cdot c = 3 \cdot - 16 = - 48$ and whose sum is $b = 8$ .

Factor $8$ out of $8 z$ .

$3 z^{2} + 8 (z) - 16$

Rewrite $8$ as $- 4$ plus $12$

$3 z^{2} + (- 4 + 12) z - 16$

Apply the distributive property.

$3 z^{2} - 4 z + 12 z - 16$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 z^{2} - 4 z) + 12 z - 16$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 z - 4$ .

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

Factor 3z^2+8z-16

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