A-LEVEL MATHEMATICS Topic : The Remainder Theorem

The Remainder Theorem is the generalized form of The Factor Theorem.
The Remainder Theorem
When a polynomial expressionis divided by a linear factorthe remainder isIfthenis a factor of
Example:
Show thatis a factor of
thereforeis a factor.
Example

If the remainder whenis divided byis 3 and the remainder whenis divided byis 4, findand
Remainder ofon division byis
Remainder when p(x) is divided byis
We solve the simultaneous equations
(1)
(2)
(1) 2*(2) givesthen from (2)
Then