If the polynomial function f(x) is divided by ( x - c ) then the remainder is equal to f(c).

ex.
evaluate f(x) = x³ - 3x² + 2x -1 at f(3) by synthetic division and the
remainder theorem.

ex.
Find the remainder of 3x³- x²+ 5x - 4 divided by (x + 2).
Use both synthetic division and the remainder theorem.

Using the remainder theorem:
Write x + 2 as x - (-2), thus f(-2), then evaluate f(x) = 3x³- x²+ 5x - 4
at f(-2).

f(-2) = 3(-2)³- (-2)²+ 5(-2) - 4
= 3(-8) - (4) + (-10) - 4
= -24 - 4 -10 - 4
= -42 the remainder is -42.

using synthetic division: