Question

The polynomial of degree 5, P(x) has a leading coefficient 1, has roots of multiplicity 2 at x=2 and x=0, and a root of multiplicity 1 at x=-4 and it goes through the point (5, 18) how do you find a formula for p(x)?

Answer 1

Such a polynomial does not exist

Explanation:

The conditions of leading coefficient 1, roots multiplicity 2 at `x=2` and `x=0` and a single root at `x=-4` are enough to define uniquely the polynomial
`p_5(x)=(x-2)^2 x^2(x+4)`
but this polynomial verifies `p_5(5)=2025 ne 18`