Top Heavy Rational Expressions (Edexcel International A Level Maths: Pure 3)

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

 

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