Question

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

Answer 1

f(-1)=f(0)=f(2)=0

f(-1) = 0 x=-1 x-1=0 (x-1)=0
f(0) =0 x=0 x-0=0 (x) =0
f(2) = 0 x=2 x-2=0 (x-2)=0

original cubic function will be the product of its roots, that is

(x)(x-1)(x-2) = 0 (x)(x-1)(x-2) = y

Answer 2

f(1)=6 means, that, whatever the cubic function is, if you set "x=1", you'd get a value of "6"

Answer 3

http://mathb.in/12758 <--- so
whatever you get from the multiplication of the roots, divide it by the (x-1)
and let's see what you get for the remainder

Answer 4

how did you get (x-1) to divide the multiplication of the roots? and also I am not very good at dividing. when you divide you have (x-1)/x^3-x^2-2x im not sure how to completely do that.