Remainder theorem

Introduction

How do we find the remainder when we divide by ?

One way is to use long division


From the long division, we get a remainder of 13

Note that:
is known as the divisor
is known as the quotient
is known as the dividend

In most cases we are only interested in the remainder, there is an easier way of obtaining the remainder without using long division

The easier way is to use the Remainder Theorem

Once again we want to find the remainder when is divided by



How do we know what value to sub in ?
If we are dividing by x - 2, we let x - 2 =0 and get x = 2. So we sub in 2
If we are dividing by x + 2, we let x + 2 =0 and get x = -2. So we sub in -2
If we are dividing by x - a, we let x - a =0 and get x = a. So we sub in a

Question 1
Given that leaves a remainder of 6 when divided by and has a factor of , find the value of a and b.


Next the question says that x + 2 is a factor
Factor means that the remainder is zero
Hence we can apply the remainder theorem


By solving the 2 simultaneous equations we can determine the values of a and b