Factor completely.
-$4 x ^ { 2 } - 14 x - 8$
A) $2 ( 2 x + 1 ) ( x - 4 )$
B) $2 ( 2 x - 1 ) ( x + 4 )$
C) prime
D) $( 4 x - 2 ) ( x + 4 )$

Question

Quizplus · Accepted Answer

The correct factorization of $4x^2 - 14x - 8$ is achieved by first factoring out the greatest common factor, which is 2, resulting in $2(2x^2 - 7x - 4)$. Then, finding two numbers that multiply to $2 \times -4 = -8$ and add to -7, which are -8 and 1, allows us to split the middle term and factor by grouping, leading to $2(2x^2 - 8x + x - 4) = 2(2x(x - 4) + 1(x - 4)) = 2(2x + 1)(x - 4)$.

Factor Completely 4x2−14x−84 x ^ { 2 } - 14 x - 84x2−14x−8

Factor Completely $4 x ^ { 2 } - 14 x - 8$