factor. $3z^2 - 4z - 7$

factor.
$3z^2 - 4z - 7$

We need two numbers that multiply to $3\times(-7)= -21$ and add up to $-4$. The numbers are $-7$ and $3$ since $-7\times3 = -21$ and $-7 + 3=-4$.

Rewrite $-4z$ as $-7z + 3z$ in the expression $3z^{2}-4z - 7$:
\[3z^{2}-7z + 3z-7\]

Group the first two terms and the last two terms:
$(3z^{2}-7z)+(3z - 7)$

Factor out $z$ from the first group and $1$ from the second group:
$z(3z - 7)+1(3z - 7)$

Factor out $(3z - 7)$ from the two terms:
$(3z - 7)(z + 1)$

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