Improper Algebraic Fractions (Edexcel International A Level (IAL) Maths: Pure 3): Revision Note

The degree of the numerator is greater than or equal to the degree of the denominator

Write as a quotient and a remainder

The algebraic equivalent of changing a top-heavy fraction to a mixed number

A polynomial f(x) of degree divided by a quadratic divisor takes the form

The quotient q will have degree 

The degree of the remainder r will be less than 

• It could be degree 1 (linear)

• Or it could be degree 0 (constant)

You still use polynomial division!

Step 1
Divide the leading term of the polynomial by the squared term of the divisor

• This gives the leading term of the quotient

Step 2
Multiply this term by the divisor

Step 3
Subtract this from the polynomial to get a new polynomial with a lower degree

Continue these steps until you have an expression with a degree lower than 2