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

Improper Algebraic Fractions

What are top-heavy (improper) rational expressions (or algrbraic fractions)?

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

How do I simplify top-heavy rational expressions?

• Write as a quotient and a remainder

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

Quadratic Divisor

What are the degrees of the quotient and remainder when a polynomial is divided by a quadratic divisor?

• Suppose a polynomial of degree is divided by a quadratic divisor

  • 

• 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)

How do I divide a polynomial by a quadratic divisor?

• You 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