Let f(x) be a polynomial. Find the remainder when f(x) is divided by x(x - 1)(x - 2), if f(0) = 0, f(1) = 1, and f(2) = 4.
Answer:x2
f(0)=0
c=0
f(1)=1,c=0, so a+b=1
f(2)=4
so 4a+2b=4
which is 2a+b=2
a+b=1
2a+b=2
so a=1, b=0
now we substitute:
a=1,b=0,c=0
x2+0x+0=x2
x2
+267 
