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

Question

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

Muhammad Saeed · Accepted Answer

Final Answer : C, Explanation :   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:   12 x 2 − 15 x + 12 x − 15 = 3 x ( 4 x − 5 ) + 3 ( 4 x − 5 ) = ( 4 x − 5 ) ( 3 x + 3 ) = ( 2 x − 3 ) ( 6 x + 5 ) 12x^2 - 15x + 12x - 15 = 3x(4x-5) + 3(4x-5) = (4x-5)(3x+3)=(2x-3)(6x+5) 12 x 2 − 15 x + 12 x − 15 = 3 x ( 4 x − 5 ) + 3 ( 4 x − 5 ) = ( 4 x − 5 ) ( 3 x + 3 ) = ( 2 x − 3 ) ( 6 x + 5 )   Therefore, the correct answer is C.

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.

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