Factor by using substitution. $8 v ^ { 4 } - 31 v ^ { 2 } + 21$
A) $\left( 8 v ^ { 2 } - 7 \right) \left( v ^ { 2 } - 3 \right)$
B) $\left( 8 v ^ { 2 } - 3 \right) \left( v ^ { 2 } - 7 \right)$
C) $\left( 8 v ^ { 2 } + 7 \right) \left( v ^ { 2 } + 3 \right)$
D) Prime

Question

Quizplus · Accepted Answer

By substituting $u = v^2$, the expression becomes $8u^2 - 31u + 21$. Factoring this quadratic gives $(8u - 7)(u - 3)$. Substituting back $v^2$ for $u$ results in $(8v^2 - 7)(v^2 - 3)$.

Factor by Using Substitution 8v4−31v2+218 v ^ { 4 } - 31 v ^ { 2 } + 218v4−31v2+21

Factor by Using Substitution $8 v ^ { 4 } - 31 v ^ { 2 } + 21$