Question

What’s is the multiplicity of f(x)=(x+3)(x-4)^2

Answer 1

The root $x=-3$ has multiplicity one and the root $x=4$ has multiplicity two.

Explanation:

Given that the function $f(x)=(x+3)(x-4)^2$

We need to determine the multiplicity of the function.

The function has 2 roots.

The roots of the function are -3 and 4.

The multiplicity of the roots means the number of times the root is a factor of the polynomial.

Thus, from the function, it is obvious that the function has the root -3 which occurs exactly once.

Thus, the root $x=-3$ has multiplicity one.

Also, the root of the function $x=4$ which occurs twice.

Thus, the root $x=4$ has multiplicity two.

Hence, the multiplicity of the function is the root $x=-3$ has multiplicity one and the root $x=4$ has multiplicity two.