Given, that a polynomial has the following:
The degree = 6
The leading coefficient = 1
The zeros are as follows:
-3 as a zero of multiplicity 3 ⇒ The corresponding factor = (x+3)
0 as a zero of multiplicity 2 ⇒ The corresponding factor = x
3 as a zero of multiplicity 1 ⇒ The corresponding factor = (x-3)
So, the equation of the polynomial written in factor form will be as follows:
[tex]f(x)=x^2(x-3)(x+3)^3[/tex]
Expand the polynomial:
[tex]\begin{gathered} f(x)=x^2(x-3)(x^3+9x^2+27x+27) \\ f(x)=(x^3-3x^2)(x^3+9x^2+27x+27) \\ f(x)=x^3(x^3+9x^2+27x+27)-3x^2(x^3+9x^2+27x+27) \\ f(x)=x^6+9x^5+27x^4+27x^3-3x^5-27x^4-81x^3-81x^2 \end{gathered}[/tex]
Combine the like terms:
So, the answer will be:
[tex]f(x)=x^6+6x^5-54x^3-81x^2[/tex]
