Factor the trinomial, if possible. 12 x 4 − 26 x 3 + 12 x 2 12 x ^ { 4 } - 26 x ^ { 3 } + 12 x ^ { 2 } 12 x 4 − 26 x 3 + 12 x 2 A) 2 x 2 ( 3 x + 2 ) ( 2 x + 3 ) 2 x ^ { 2 } ( 3 x + 2 ) ( 2 x + 3 ) 2 x 2 ( 3 x + 2 ) ( 2 x + 3 ) B) 2 x 2 ( 3 x − 2 ) ( 2 x − 3 ) 2 x ^ { 2 } ( 3 x - 2 ) ( 2 x - 3 ) 2 x 2 ( 3 x − 2 ) ( 2 x − 3 ) C) 2 x 2 ( 3 x + 2 ) ( 2 x − 3 ) 2 x ^ { 2 } ( 3 x + 2 ) ( 2 x - 3 ) 2 x 2 ( 3 x + 2 ) ( 2 x − 3 ) D) 2 x 2 ( 3 x − 2 ) ( 2 x + 3 ) 2 x ^ { 2 } ( 3 x - 2 ) ( 2 x + 3 ) 2 x 2 ( 3 x − 2 ) ( 2 x + 3 ) E) The trinomial is prime.

Question

Factor the trinomial, if possible.   12 x 4 − 26 x 3 + 12 x 2 12 x ^ { 4 } - 26 x ^ { 3 } + 12 x ^ { 2 } 12 x 4 − 26 x 3 + 12 x 2 A)    2 x 2 ( 3 x + 2 )  ( 2 x + 3 )  2 x ^ { 2 } ( 3 x + 2 )  ( 2 x + 3 )  2 x 2 ( 3 x + 2 )  ( 2 x + 3 )  B)    2 x 2 ( 3 x − 2 )  ( 2 x − 3 )  2 x ^ { 2 } ( 3 x - 2 )  ( 2 x - 3 )  2 x 2 ( 3 x − 2 )  ( 2 x − 3 )  C)    2 x 2 ( 3 x + 2 )  ( 2 x − 3 )  2 x ^ { 2 } ( 3 x + 2 )  ( 2 x - 3 )  2 x 2 ( 3 x + 2 )  ( 2 x − 3 )  D)    2 x 2 ( 3 x − 2 )  ( 2 x + 3 )  2 x ^ { 2 } ( 3 x - 2 )  ( 2 x + 3 )  2 x 2 ( 3 x − 2 )  ( 2 x + 3 )  E) The trinomial is prime.

courtney wilson · Accepted Answer

Final Answer : B, Explanation :   First, factor out the greatest common factor, which is   2 x 2 2x^2 2 x 2  , giving   2 x 2 ( 6 x 2 − 13 x + 6 ) 2x^2(6x^2 - 13x + 6) 2 x 2 ( 6 x 2 − 13 x + 6 )  . Factoring the quadratic inside the parentheses results in   2 x 2 ( 3 x − 2 ) ( 2 x − 3 ) 2x^2(3x - 2)(2x - 3) 2 x 2 ( 3 x − 2 ) ( 2 x − 3 )  , matching option B.

Factor the trinomial, if possible. $12 x ^ { 4 } - 26 x ^ { 3 } + 12 x ^ { 2 }$

A) $2 x ^ { 2 } ( 3 x + 2 ) ( 2 x + 3 )$
B) $2 x ^ { 2 } ( 3 x - 2 ) ( 2 x - 3 )$
C) $2 x ^ { 2 } ( 3 x + 2 ) ( 2 x - 3 )$
D) $2 x ^ { 2 } ( 3 x - 2 ) ( 2 x + 3 )$
E) The trinomial is prime.

Definitions

Learning Objectives

Learning Objectives

Related questions