Answer:
P(x) = x²(x +1)(x -2)²
Explanation:
You want the 5th degree polynomial with leading coefficient 1 that has roots of 0 and 3, each with multiplicity 2, and a root of -1.
Factors
You recall that a polynomial with root p has (x -p) as a factor. A root that is repeated m times has multiplicity m.
You recall that an exponent is used to signify the number of times a factor is repeated.
The factored form of P(x) is then ...
P(x) = (x -2)²(x -0)²(x -(-1)) . . . . . roots 2 and 0 repeated twice, root -1
P(x) = x²(x +1)(x -2)²
__
Additional comment
If you like, you can multiply it out and collect terms. The result will be ...
P(x) = x⁵ -3x⁴ +4x²