Factor using the ac-method.
-$10 z ^ { 2 } + 9 z - 9$
A) $( 10 z + 3 ) ( z - 3 )$
B) $( 2 z - 3 ) ( 5 z + 3 )$
C) prime
D) $( 2 z + 3 ) ( 5 z - 3 )$

Question

Quizplus · Accepted Answer

The ac-method involves multiplying the coefficient of $z^2$ (which is 10) by the constant term (-9), giving -90. We then find two numbers that multiply to -90 and add to the middle coefficient (9). These numbers are 15 and -6. We rewrite the middle term using these numbers: $10z^2 + 15z - 6z - 9$. Factoring by grouping gives us $5z(2z + 3) - 3(2z + 3)$, which simplifies to $(2z + 3)(5z - 3)$.

Factor Using the Ac-Method 10z2+9z−910 z ^ { 2 } + 9 z - 910z2+9z−9

Factor Using the Ac-Method $10 z ^ { 2 } + 9 z - 9$