Find the zeros of the polynomial function and state the multiplicity of each.
-$$f ( x ) = \left( x ^ { 2 } + 12 x + 32 \right) ^ { 2 }$$
A) $- 2$ (multiplicity 4)
B) 8 (multiplicity 2), 4 (multiplicity 2 )
C) $- 4$ (multiplicity 2 ), $- 8$ (multiplicity 2 )
D) 2 (multiplicity 2), $- 2$ (multiplicity 2 )

Question

Quizplus · Accepted Answer

First, factor the quadratic inside the parentheses: $x^2 + 12x + 32 = (x + 4)(x + 8)$. Since the entire expression is squared, each root ($-4$ and $-8$) has a multiplicity of 2.

Find the Zeros of the Polynomial Function and State the Multiplicity