If a*x^3 + b*x^2 + c*x + d is divided by (x - 2), then what is the remainder?

You need to remember the reminder theorem such
that:

`f(x) = (x-2)*q(x) +
r(x)`

q(x) and r(x) express the quotient and reminder
you'll get after division.

You should substitute 2 for x in
equation above such that:

`f(2) = (2-2)*q(2) +
r(2)`

Notice that you may evaluate f(2) substituting 2 for
x in equation of polynomial such that:

`f(2) = 8a + 4b + 2c
+ d`

You need to substitute`8a + 4b + 2c + d ` for f(2) in
equation `f(2) = (2-2)*q(2) + r(2)`  such that:

`8a + 4b +
2c + d = 0*q(2) + r(2)`

`r(2) = 8a + 4b + 2c +
d`

Hence, evaluating the reminder r(x) at
x=2, under given conditions, yields `r(2) = 8a + 4b + 2c + d`
.