Factor using the ac-method.
-$15 x ^ { 2 } + 19 x + 6$
A) $( 15 x + 2 ) ( x + 3 )$
B) prime
C) $( 3 x + 2 ) ( 5 x + 3 )$
D) $( 3 x - 2 ) ( 5 x - 3 )$

Question

Quizplus · Accepted Answer

Using the ac-method, we need to find two numbers whose product is 15*6=90 and whose sum is 19. The only two numbers that satisfy this are 5 and 18. Therefore, we can rewrite the middle term as 5x+18x. 
\begin{align*}
15 x ^ { 2 } + 19 x + 6 &= 15 x ^ { 2 } + 5 x + 18 x + 6 \ 
&= 5 x (3x+1) + 6(3x+1)\
&= (5x+6)(3x+1)\
&= (3x+2)(5x+3)
\end{align*}
Choice C matches this factorization.

Factor Using the Ac-Method 15x2+19x+615 x ^ { 2 } + 19 x + 615x2+19x+6

Factor Using the Ac-Method $15 x ^ { 2 } + 19 x + 6$