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

When you have \(\large\color{blue}{ a \times b=0 }\), then either \(\large\color{black}{ a =0 }\) or, \(\large\color{black}{ b=0 }\).

Answer 2

This is called a zero product property.

Answer 3

Here, you got a similar thing,
(because you want to find the zeros of the function, you set \(\large\color{black}{ f(x) =0 }\) )

\(\large\color{blue}{ 0= 5(x + 8)^2(x - 8)^3 }\)

So, either \(\large\color{black}{ 0= (x + 8)^2 }\) or \(\large\color{black}{ 0= (x - 8)^3 }\)

Answer 4

@SolomonZelman the answer choices are
A) 4, multiplicity 1; -8, multiplicity 3; 8, multiplicity 3
B) -8, multiplicity 2; 8, multiplicity 3
C) -8, multiplicity 3; 8, multiplicity 2
D) 4, multiplicity 1; 8, multiplicity 1; -8, multiplicity 1

so would it be c?