Factor the trinomial, if possible. $12 x ^ { 2 } - 8 x - 15$
A) $( 2 x - 3 ) ( 6 x - 5 )$
B) $( 2 x + 3 ) ( 6 x + 5 )$
C) $( 2 x - 3 ) ( 6 x + 5 )$
D) $( 3 x + 2 ) ( 5 x - 6 )$
E)The trinomial is prime.

Question

Quizplus · Accepted Answer

To find the factors, first multiply the coefficient of the leading term (12) by the constant term (-15) to get -180. Next, find two factors of -180 that add up to the coefficient of the middle term (-8). It turns out that these factors are -15 and 12. Then, split the middle term -8x into -15x + 12x, so the trinomial becomes: $$12x^2 - 15x + 12x - 15 = 3x(4x-5) + 3(4x-5) = (4x-5)(3x+3)=(2x-3)(6x+5)$$ Therefore, the correct answer is C.

Factor the Trinomial, If Possible 12x2−8x−1512 x ^ { 2 } - 8 x - 1512x2−8x−15

Factor the Trinomial, If Possible $12 x ^ { 2 } - 8 x - 15$