Find the remainder of the division problem shown below.

(x^4 - x^3 + 3x - 3) / (x-2)

by using the Remainder Theorem,
x-2 = 0
x = 2

substitute x=2 into x^4 - x^3 + 3x - 3,
2^4 - 2^3 + 3(2) - 3
= 11

therefore the remainder is 11...

this formula is derived from...
p(x) as initial polynomial function... (dividend)
g(x) as divisor
q(x) as quotient function
r(x) as remainder

p(x)/g(x) = q(x) + r(x)/g(x)
p(x) = q(x)g(x) + r(x)

in this case, g(x) = x-2
when x = 2, g(x) = 0
when g(x) = 0
p(x) = r(x)
therefore p(2) = r(x)
r(x) = 11

hope this helps...