Find the zeros of the polynomial function and state the multiplicity of each.
-$5 x ( x + 6 ) \left( x ^ { 2 } - 16 \right) ^ { 3 }$
A) 0 (multiplicity $1 ), - 6$ (multiplicity $1 ), \pm 4$ (multiplicity 1 )
B) 0 (multiplicity 1), $- 6$ (multiplicity 1 ), $- 16$ (multiplicity 3 )
C) 0 (multiplicity 1), 6 (multiplicity 1), $\pm 4$ (multiplicity 3)
D) 0 (multiplicity 1 ), $- 6$ (multiplicity $1 ), \pm 4$ (multiplicity 3 )

Question

Quizplus · Accepted Answer

The zeros of the polynomial are found by setting each factor equal to zero: $5x=0$ gives $x=0$ with multiplicity 1, $x+6=0$ gives $x=-6$ with multiplicity 1, and $(x^2-16)^3=0$ gives $x^2-16=0$ which further gives $x=\pm4$ with multiplicity 3, as the factor is raised to the third power.

Find the Zeros of the Polynomial Function and State the Multiplicity