Factor using the ac-method.
-$- 24 x ^ { 2 } - 20 x + 24$
A) $( - 12 x + 8 ) ( 2 x + 3 )$
B) $- 4 ( 3 x - 2 ) ( 2 x + 3 )$
C) $- 4 ( 3 x + 2 ) ( 2 x - 3 )$
D) prime

Question

Quizplus · Accepted Answer

To factor using the ac-method, we need to find two numbers whose product is the product of the coefficient of the first term and the constant term, and whose sum is the coefficient of the middle term. Product of the coefficient of the first term and the constant term is $(-24)(24) = -576$ and the coefficient of the middle term is $(-20)$.
We need to find two numbers that give the product of $-576$ and sum of $-20$. The numbers are $(-24)$ and $24$.
Split the middle term of the polynomial $ - 24 x ^ { 2 } - 20 x + 24$ using the two numbers found above:
\begin{align*}
- 24 x ^ { 2 } - 20 x + 24 &= -24x^2 + 24x -44x + 24\
& = -4 ( 6 x ^ { 2 } - 6 x - 6 x + 6 )\
& = -4 ( 6 x ( x - 1 ) - 6 ( x - 1 ) )\
& = -4 ( 6 x - 6 ) ( x - 1 )\
& = -4 ( 3 x - 3 ) ( 2 x + 3 )
\end{align*}
Therefore, the factored form using the ac-method is $-4 (3x-2)(2x+3)$. The option B is the correct answer.

Factor Using the Ac-Method −24x2−20x+24- 24 x ^ { 2 } - 20 x + 24−24x2−20x+24

Factor Using the Ac-Method $- 24 x ^ { 2 } - 20 x + 24$