Factor the trinomial, if possible.
-$$12 z ^ { 2 } + 7 z - 12$$
A) $( 12 z - 3 ) ( z - 12 )$
B) $( 4 \mathrm { z } + 3 ) ( 3 \mathrm { z } - 4 )$
C) $( 12 z - 3 ) ( z + 4 )$
D) $( 4 z - 3 ) ( 3 z + 4 )$

Question

Quizplus · Accepted Answer

To factor the trinomial $12z^2 + 7z - 12$, we look for two numbers that multiply to $12 \times -12 = -144$ and add to $7$. The numbers $16$ and $-9$ work since $16 \times -9 = -144$ and $16 - 9 = 7$. Rewriting the middle term $7z$ as $16z - 9z$ gives us $12z^2 + 16z - 9z - 12$, which can be factored by grouping into $(4z - 3)(3z + 4)$.

Factor the Trinomial, If Possible 12z2+7z−1212 z ^ { 2 } + 7 z - 1212z2+7z−12

Factor the Trinomial, If Possible $12 z ^ { 2 } + 7 z - 12$