A Level Maths Notes: C4 - Long Division of Polynomials
remainder
1 or
3
is the quotient and 1 the remainder. It is not just pure numbers that
can undergo long division. So can polynomials. In the example below
it is shown how to find the quotient and remainder of
Note
that we must write the numerator and denominator to include all the
coefficients of
up
to the highest power in the numerator and up to the highest power in
the denominator, so that we write
as
At each stage we work to eliminate the highest power of
To
start with the highest power of
is
4: multiply the denominator
by
–
the first term of the quotient - to get
and
subtract from the numerator to get
Now
the highest power ofis
3. We multiply the denominator by
–
the nest term of the quotient - to get
and
subtract to get
The
highest power ofis
2. We multiply the denominator by 2 – the last term in the quotient
- to get
and
subtract to get zero. Hence
There
is no remainder.
If instead we are finding the quotient and remainder of
we
follow the same process, but now, as shown below, the remainder is 9
hence the division is now
hence