Question

Find the multiplicity of each zero of the function.

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

What is the multiplicity of the zero x= -3
What is the multiplicity of the zero x= 4

I looked at a few multiplicity problems but none of them looked like my problems, so I was just confused.
Do I just plug in the -3 and the 4? Sorry if that's a dumb question, but I just want to be sure.
If anyone can help me start off the problem I would appreciate it.

Answer 1

the power of the factor is the multiplicity of the root -- the number of times the factor appears.
So, -3 has multiplicity 2
4 has multiplicity 3

Answer 2

Ohhhhhhhhhh

so, x+3=0 -> x=-3 and it has a multiplicity 2 since it's to the power of 2
x-4=0 -> x=4 and it has a multiplicity of 3 since it's to the power of 3
Is that correct?

Yeah, the problems I was looking at are totally different, so I just ended up overthinking this. Thank you!