What is the reminder if ax^3+bx^2+cx+d is divided by x-2 ?

Since the polynomial is divided by the binomial x-2, the
reminder is a constant.

We'll write the division with
reminder:

ax^3+bx^2+cx+d = (x-2)(ex^2 + fx + g) +
h

The reminder R(x) = h

The fundamental
theorem of algebra states that the reminder of a polynomial divided by a binomial x-a
is:

P(a) = R(a)

We'll substitute x by 2
in the expression of polynomial:

P(2) =
a*2^3+b*2^2+c*2+d

P(2) = 8a + 4b + 2c +
d

The reminder is:

R(2) =
8a + 4b + 2c + d