Find the zeros of the polynomial function and state the multiplicity of each.
-$$f ( x ) = - 5 x ^ { 2 } ( x - 8 ) ( x + 4 ) ^ { 3 }$$
A) $- 4$ (multiplicity 1), 4 (multiplicity 1 ), 8 (multiplicity 1 )
B) $- 4$ (multiplicity 3), 0 (multiplicity 2), 4 (multiplicity 1), 8 (multiplicity 1)
C) $- 4$ (multiplicity 3), 8 (multiplicity 1 )
D) $- 4$ (multiplicity 3), 0 (multiplicity 2), 8 (multiplicity 1 )

Question

Quizplus · Accepted Answer

The zeros are found by setting each factor to zero: $x^2$ gives zero with multiplicity 2, $x - 8$ gives 8 with multiplicity 1, and $(x + 4)^3$ gives -4 with multiplicity 3.

Find the Zeros of the Polynomial Function and State the Multiplicity