Factor 7z^2-4z-3

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

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

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

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

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

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 z + 3$ .

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

Factor 7z^2-4z-3

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