Question

find an expression for a cubic function f if f(1)=6 and f(-1)=f(0)=f(2)=0

Answer 1

from f(0) = 0 and f(2) = 0 and f(-1)=0
we know that there are 3 factors,
x(x-2)(x+1)
Since it is a cubic, there should be a third factor, let it be
ax + b)
so
f(x) = x(x-2)(x+1)
BUT, (1,6) does not satisfy this, so we must include a constant a , so that

f(x) = ax(x-2)(x+1)
for (1,6) to lie on it
6 = a(1)(1-2)(1+1)
6 = -2a
a = -3

f(x) = -3x(x-2)(x+1)

Answer 2

Very good