Factor 3z^2+2z-16

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

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 $b = 2$ .

Factor $2$ out of $2 z$ .

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

Rewrite $2$ as $- 6$ plus $8$

$3 z^{2} + (- 6 + 8) z - 16$

Apply the distributive property.

$3 z^{2} - 6 z + 8 z - 16$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 z^{2} - 6 z) + 8 z - 16$

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

$3 z (z - 2) + 8 (z - 2)$

Step 3

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

$(z - 2) (3 z + 8)$

Factor 3z^2+2z-16

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