Question

Find the zeros of the polynomial function and state the multiplicity of each. f(x) = 5(x + 8)2(x - 8)3

Answer 1

well all you need for the zeros is to solve

x - 8 = 0

and

x + 8 = 0

multiplicity is the number of times the factor occurs...

so look at the powers of each factor

Answer 2

\(\bf f(x) = 5(x + 8)^2(x - 8)^3\\
\textit{setting y = 0, we get}\\
0 = 5(x + 8)^2(x - 8)^3\\
\textit{solve for }\quad x \quad \textit{keep in mind that}\\
5(x + 8)^2(x - 8)^3\implies 5(x + 8)(x + 8)(x - 8)(x - 8)(x - 8)\)