Find the zeros of the polynomial function and state the multiplicity of each.
-$$f ( x ) = 5 x ( x - 7 ) ^ { 3 } \left( x ^ { 2 } - 16 \right)$$
A) 0 (multiplicity 1), - 16 (multiplicity 2), 7 (multiplicity 3 )
B) 0 (multiplicity 1), $\pm 4$ (multiplicity 2), $- 7$ (multiplicity 3 )
C) 0 (multiplicity 1), $\pm 4$ (multiplicity 1), 7 (multiplicity 3 )
D) $\pm 4$ (multiplicity 1), 7 (multiplicity 3 )

Question

Quizplus · Accepted Answer

The zeros of the polynomial can be found by setting each factor equal to zero. The factor $5x$ gives a zero at $x = 0$ with multiplicity 1. The factor $(x - 7)^3$ gives a zero at $x = 7$ with multiplicity 3. The factor $(x^2 - 16)$ can be factored further into $(x + 4)(x - 4)$, giving zeros at $x = \pm 4$ each with multiplicity 1.

Find the Zeros of the Polynomial Function and State the Multiplicity