Factor 3z^2-4z-7

$3 z^{2} - 4 z - 7$

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 $a \cdot c = 3 \cdot - 7 = - 21$ and whose sum is $b = - 4$ .

Factor $- 4$ out of $- 4 z$ .

$3 z^{2} - 4 (z) - 7$

Rewrite $- 4$ as $3$ plus $- 7$

$3 z^{2} + (3 - 7) z - 7$

Apply the distributive property.

$3 z^{2} + 3 z - 7 z - 7$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 z^{2} + 3 z) - 7 z - 7$

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

$3 z (z + 1) - 7 (z + 1)$

Step 3

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

$(z + 1) (3 z - 7)$

Factor 3z^2-4z-7

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