Question

Find a polynomial of degree 3 with a real coefficient that satisfies the given condition. Zeros: -2, 1, 0; f(2)=32

Answer 1

Its factors would be
(x+2)*(x-1)*(x+0)

x^2 +x -2

x^3 + 0 + x^2 + 0 -2x +0

Equation: x^3 + x^2 -2x
f(2) = 8 + 4 -4

2x^3  + 2x^2  -4x +0
f(2) = 16 + 8 -8

3x^3  + 3x^2  -6x +0
f(2) =  24 +12 -12

4x^3  + 4x^2  -8x +0
f(2) =  32 +16 -16

So, the equation is:
4x^3  + 4x^2  -8x = 0