Factor using the ac-method.
-$$8 z ^ { 2 } + 6 z - 9$$
A) $( 8 z + 3 ) ( z - 3 )$
B) prime
C) $( 2 z + 3 ) ( 4 z - 3 )$
D) $( 2 z - 3 ) ( 4 z + 3 )$

Question

Quizplus · Accepted Answer

The ac-method involves multiplying the coefficient of $z^2$ (which is 8) by the constant term (which is -9), giving -72. We then find two numbers that multiply to -72 and add to the coefficient of $z$ (which is 6). These numbers are 12 and -6. We rewrite the middle term (6z) as 12z - 6z and factor by grouping, leading to the correct factorization $(2z + 3)(4z - 3)$.

Factor Using the Ac-Method 8z2+6z−98 z ^ { 2 } + 6 z - 98z2+6z−9

Factor Using the Ac-Method $8 z ^ { 2 } + 6 z - 9$