Factor by using substitution. $$4 ( 4 t - 1 ) ^ { 2 } + 18 ( 4 t - 1 ) + 8$$
A) $( 4 t + 2 ) ( t + 4 )$
B) $2 ( 8 t - 1 ) ( 4 t + 3 )$
C) $2 ( 8 t + 1 ) ( 4 t - 3 )$
D) Prime

Question

Quizplus · Accepted Answer

By substituting $u = 4t - 1$, the expression becomes $4u^2 + 18u + 8$. Factoring this quadratic expression gives $2(2u + 1)(2u + 4)$. Substituting back $u = 4t - 1$ results in $2(8t - 1)(4t + 3)$, which corresponds to choice B.

Factor by Using Substitution 4(4t−1)2+18(4t−1)+84 ( 4 t - 1 ) ^ { 2 } + 18 ( 4 t - 1 ) + 84(4t−1)2+18(4t−1)+8

Factor by Using Substitution $4 ( 4 t - 1 ) ^ { 2 } + 18 ( 4 t - 1 ) + 8$