Answer:
According to the given information, the polymomial expression should have the following factors.
Root of -6 and multiplicity of 1: [tex](x+6)[/tex]
Root of -2 and multiplicity of 3: [tex](x+2)^{3}[/tex]
Root of 0 with a multiplicity of 2: [tex]x^{2}[/tex]
Root of 4 and multiplicity of 3: [tex](x-4)^{3}[/tex]
If we sum exponents, we can know the grade of the polnomial:
1 + 3 + 2 + 3 = 9
So, the grade of the polynomial function is 9, which makes it an odd function.
Additionally, the function is
[tex]f(x)=(x+6)x^{2}(x+2)^{3}(x-4)^{3}[/tex]
Its graph is attached.
