Use substitution to factor the polynomial completely.
-$$( x + 7 ) ^ { 2 } - 10 ( x + 7 ) + 16$$
A) $\left( x ^ { 2 } - 7 x + 8 \right) \left( x ^ { 2 } - 7 x + 2 \right)$
B) $\left( x ^ { 2 } + 7 x - 8 \right) \left( x ^ { 2 } + 7 x - 2 \right)$
C) $( x + 15 ) ( x + 9 )$
D) $( x - 1 ) ( x + 5 )$

Question

Quizplus · Accepted Answer

Let $u = x + 7$. The given polynomial becomes $u^2 - 10u + 16$, which factors as $(u - 2)(u - 8)$. Substituting back $x + 7$ for $u$, we get $(x + 7 - 2)(x + 7 - 8)$ or $(x + 5)(x - 1)$.

Use Substitution to Factor the Polynomial Completely (x+7)2−10(x+7)+16( x + 7 ) ^ { 2 } - 10 ( x + 7 ) + 16(x+7)2−10(x+7)+16

Use Substitution to Factor the Polynomial Completely $( x + 7 ) ^ { 2 } - 10 ( x + 7 ) + 16$