Question

Question #45160

Answer 1

See explanation.

Explanation:

To solve this task you need to use the folloing feature of polynomial:

If `a` is a zero of polynomial with multiplicity `n`, then the polynomial is divisible by `(x-a)^n` and not divisible by `(x-a)^(n+1)`

As stated above the polynomial would have to be divisible by `(x-3)^3`, and `(x-0)^2`. The only polynomial of degree `5` fulfilling theses conditions is:

`P(x)=(x-3)^3*x^2=(x^3+3x^2+3x+1)*x^2`
`=x^5+3x^4+3x^3+x^2`