The polynomial is of the form:
[tex]P(x)=a (x+b)^{2}(x-c)
[/tex]
We are provided with the two zeros in the question statement. The zero with multiplicity 2 is -3, and zero with multiplicity 1 is 2. So using these values, the polynomial becomes:
[tex]P(x)=a (x+3)^{2}(x-2) [/tex]
The polynomial also passes from the point (0,36). This mean if we substitute x=0, the answer should be 36.
[tex]P(0)=36=a (0+3)^{2}(0-2) \\ \\
36=a(9)(-2) \\ \\
36=-18a \\ \\
a=-2 [/tex]
Thus the value of a for given polynomial will be -2. The complete equation of polynomial will be:
[tex]P(x)=-2 (x+3)^{2}(x-2)[/tex]
