Factor using the ac-method.
-$15 x ^ { 2 } + 22 x + 8$
A) $( 15 x + 2 ) ( x + 4 )$
B) $( 3 x - 2 ) ( 5 x - 4 )$
C) prime
D) $( 3 x + 2 ) ( 5 x + 4 )$

Question

Quizplus · Accepted Answer

The ac-method involves multiplying the coefficient of $x^2$ (which is 15) by the constant term (which is 8), giving 120. We then find two numbers that multiply to 120 and add to the middle coefficient, 22. These numbers are 10 and 12. We rewrite the middle term using these numbers: $15x^2 + 10x + 12x + 8$. Factoring by grouping, we get $5x(3x + 2) + 4(3x + 2)$, which simplifies to $(3x + 2)(5x + 4)$.

Factor Using the Ac-Method 15x2+22x+815 x ^ { 2 } + 22 x + 815x2+22x+8

Factor Using the Ac-Method $15 x ^ { 2 } + 22 x + 8$