Find the zeros of the polynomial function and state the multiplicity of each.
-$$f ( x ) = 3 ( x + 8 ) ^ { 2 } ( x - 8 ) ^ { 3 }$$
A) $- 8$ (multiplicity 2 ), 8 (multiplicity 3 )
B) $- 8$ (multiplicity 3), 8 (multiplicity 2 )
C) 4 (multiplicity 1), 8 (multiplicity 1), $- 8$ (multiplicity 1 )
D) 4 (multiplicity 1), $- 8$ (multiplicity 3), 8 (multiplicity 3)

Question

Quizplus · Accepted Answer

The zeros of the polynomial are found by setting $f(x) = 0$. This gives us the zeros at $x = -8$ and $x = 8$. The multiplicity of each zero is determined by the exponent of its corresponding factor in the polynomial. Thus, $-8$ has a multiplicity of 2 because of the factor $(x + 8)^2$, and $8$ has a multiplicity of 3 because of the factor $(x - 8)^3$.

Find the Zeros of the Polynomial Function and State the Multiplicity