Find a polynomial of the specified degree that satisfies the given conditions.

Question

Degree 4; zeros −3, 0, 1, 4; coefficient of x3 is 4

Answer 1

zeros −3, 0, 1, 4 -->x(x+3)(x-1)(x-4)

expanding this gives us
x^4 - 2x^3 - 11x^2 + 12x

but we are told that the x^3 terms is 4x^3
and we have it as -2x^3
so there had to be a -2 in front of the whole mess

polynomial is -2x(x-1)(x-4)(x+3)
or
-2x^4 + 4x^3 + 22x^2 - 24x