Factor using the ac-method.
-$36 x ^ { 2 } + 21 x y + 3 y ^ { 2 }$
A) $( 9 x + 3 y ) ( 4 x + y )$
B) $3 ( 3 x - y ) ( 4 x - y )$
C) prime
D) $3 ( 3 x + y ) ( 4 x + y )$

Question

Quizplus · Accepted Answer

The expression can be factored by first factoring out the greatest common factor (GCF), which is 3, resulting in $3(12x^2 + 7xy + y^2)$. Then, by applying the ac method (where a=12, b=7, and c=1 in the quadratic expression ax^2+bx+c), we look for two numbers that multiply to ac (12*1=12) and add to b (7). These numbers are 3 and 4. Rewriting the middle term (7xy) as 3xy + 4xy and factoring by grouping gives us $3(3x+y)(4x+y)$.

Factor Using the Ac-Method 36x2+21xy+3y236 x ^ { 2 } + 21 x y + 3 y ^ { 2 }36x2+21xy+3y2

Factor Using the Ac-Method $36 x ^ { 2 } + 21 x y + 3 y ^ { 2 }$