By the given properties of the polynomial
The polynomial is of fifth-degree
This implies that the highest power of the variable is 5
Also, we are given that
2 is a zero of multiplicity 3,
For 2 to be a zero of a polynomial then the expression
[tex]x-2[/tex]
is a factor of the polynomial
Since the multiplicity is 3 then the expression becomes
[tex](x-2)^3[/tex]
Also, -2 is the only other zero
This implies,
[tex]x+2[/tex]
is a factor of the polynomial
For the polynomial to be of fifth-degree then the factor x + 2 becomes
[tex](x+2)^2[/tex]
The leading coefficient of the polynomial is 5
Therefore, the polynomial is
[tex]y=5(x-2)^3(x+2)^2[/tex]
