Okay, here we have this:
We need to find the zeros and it's multiplicity of the following polynomial:
[tex]f(x)=5x(x-4)(x+9)^2(x+3)[/tex]
So, considering that in a function of the following form:
[tex]f(x)=a\cdot(x-x_0)^{m_0}(x-x_1)^{m_1}\cdot\ldots\cdot(x-x_n)^{m_n}[/tex]
The zeros will be: x₀, x₁, ..., xn
The multiplicities are:
[tex]m_0,^{}m_1,\ldots,\text{ }m_n[/tex]
In this case we obtain that the zeros with their respectives multiplicities are:
Zeros of multiplicity one: 0, 4, -3
Zeros of multiplicity two: -9
