Question

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

f(x) = 4(x + 7)2(x - 7)3

Answer 1

f(x) will be zero when either of the factors is zero.
x+7 = 0 or (x-7) = 0
solve for x.

Answer 2

\[
f(x) = 4(x+7)^2(x-7)^3 \\
(x+7)^2 = 0 \text{ or } (x-7)^3 = 0 \\
x = -7 \text{ or } x = 7 \text{ are the roots.} \\
\text{Since } (x+7)^2 = 0, x = -7 \text{ has a multiplicity of 2} \\
\text{Since } (x-7)^3 = 0, x = 7 \text{ has a multiplicity of 3}
\]

Answer 3

Thank you!!!!