If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
-$$12 x ^ { 2 } - 52 x - 40$$
A) $4 ( 3 x + 2 ) ( x - 5 )$
B) $4 ( 3 x - 2 ) ( x + 5 )$
C) $12 x ^ { 2 } - 52 x - 40$
D) $( 12 x + 8 ) ( x - 5 )$

Question

Quizplus · Accepted Answer

First, factor out the greatest common factor (GCF), which is 4, giving $4(3x^2 - 13x - 10)$. Then, find two numbers that multiply to $3 \times -10 = -30$ and add to -13, which are -15 and +2. Rewrite the middle term using these numbers and factor by grouping, leading to $4(3x^2 - 15x + 2x - 10)$, which simplifies to $4(3x(x - 5) + 2(x - 5)) = 4(3x + 2)(x - 5)$.

If Possible, Factor the Polynomial Completely 12x2−52x−4012 x ^ { 2 } - 52 x - 4012x2−52x−40

If Possible, Factor the Polynomial Completely $12 x ^ { 2 } - 52 x - 40$