Question

Find the zeros of the polynomial function and state the multiplicity of each.

f(x) = 3(x + 8)^2(x - 8)^3

Answer 1

set y = 0
that's why is called the "zeros of the polynomial"
which is really just where the x-axis is touched by the graph, or the x-intercepts

Answer 2

\(\bf y = 3(x + 8)^2(x - 8)^3\implies 0= 3(x + 8)^2(x - 8)^3\\ \quad \\
0 = (x + 8)^2(x - 8)^3\\ \quad \\
0 = (x + 8)(x + 8)(x - 8)(x - 8)(x - 8)\)

Answer 3

-8, multiplicity 3; 8, multiplicity 2 ? @jdoe0001