Factor by using substitution. $$( 5 x + 7 ) ^ { 2 } - 5 ( 5 x + 7 ) - 24$$
A) $5 ( 5 x + 1 ) ( x - 2 )$
B) $5 ( 5 x - 1 ) ( x + 2 )$
C) $5 ( 5 x - 1 ) ( x - 2 )$
D) Prime

Question

Quizplus · Accepted Answer

By substituting $u = 5x + 7$, the expression becomes $u^2 - 5u - 24$, which factors to $(u-8)(u+3)$. Substituting back $5x + 7$ for $u$, we get $(5x + 7 - 8)(5x + 7 + 3)$ simplifying to $(5x - 1)(5x + 10)$. Factoring out a 5 from the second term gives $5(5x - 1)(x + 2)$.

Factor by Using Substitution (5x+7)2−5(5x+7)−24( 5 x + 7 ) ^ { 2 } - 5 ( 5 x + 7 ) - 24(5x+7)2−5(5x+7)−24

Factor by Using Substitution $( 5 x + 7 ) ^ { 2 } - 5 ( 5 x + 7 ) - 24$