Question

Which statement about the function below is true?

f(x) = x^3 - 5x^2 - 25x + 125 = (x + 5)(x - 5)(x 5)

The root 5 has a multiplicity of 1.

The root 5 has a multiplicity of 2.

The root 5 has a multiplicity of 1.

The root 5 has a multiplicity of 3.

Answer 1

First, when you make a post, proof it.
Notice that you left off a sign in your posted question: (x + 5)(x - 5) -->(x 5)

Answer 2

So, I factored the expression:

If you solve this: (x - 5)(x - 5)(x + 5) = 0

By the Zero Product Property:

x - 5 = 0 OR x - 5 = 0 OR x + 5 = 0

So, solve each of those linear equations for x.

Then, you will know the multiplicity of the roots.

Answer 3

@bob8590