SOLUTION
Write out the equation given
[tex]y=x^2(x-3)^3[/tex]The zeros of the polynomial is obtain by equating the polynomial to zero.
Hence
[tex]x^2(x-3)^3=0[/tex]Equate each product to zero, we have
[tex]\begin{gathered} x=0\text{ or x-3=0} \\ x=0,\text{ x=3} \end{gathered}[/tex]The zeros of the polynomial are
[tex]0,\text{ and 3}[/tex]The zeros of the polynomials is 0 and 3
the multiplicity of multiple zeros is the number of times the zeros of the polynomial occur which is obtain from the degree of each terms in the polynomial.
Hence
[tex]\begin{gathered} x^2 \\ \operatorname{mean}s\text{ x=0 occurs twice} \end{gathered}[/tex]Then
x =0 has the multiplicity of 2
For
[tex]\begin{gathered} (x-3)^3 \\ \operatorname{mean}s\text{ (x-3) occurs thrice} \end{gathered}[/tex]x = 3 has a multiplicity of 3
