## Long Division of Polynomials

At each stage we work to eliminate the highest power ofTo start with the highest power ofis 4: multiply the denominatorby– the first term of the quotient - to getand subtract from the numerator to getNow the highest power ofis 3. We multiply the denominator by– the nest term of the quotient - to getand subtract to getThe highest power ofis 2. We multiply the denominator by 2 – the last term in the quotient - to getand subtract to get zero. HenceThere is no remainder.

If instead we are finding the quotient and remainder ofwe follow the same process, but now, as shown below, the remainder is 9 hence the division is now

hence