Polynomial Division (Cambridge O Level Additional Maths)

What is polynomial division?

• Polynomial division is the process of dividing two polynomials
  • This is usually only useful when the degree of the denominator is less than or equal to the degree of the numerator

• Polynomial division is a method for splitting polynomials into factor pairs
  • (with or without a remainder term)

• The main uses of polynomial division are
  • factorising polynomials
  • simplifying 'top-heavy' algebraic fractions

How do I divide polynomials?

• The method used for polynomial division is just like the long division method for numbers
  • sometimes called the 'bus stop method'

• The answer to a polynomial division question is built up term by term
  • Start by dividing by the highest power term
  • Write out this multiplied by the divisor and subtract

•  Continue to divide by each reducing power term and subtracting your answer each time

•  Continue until you are left with zero

• If the divisor is not a factor of the polynomial then there will be a remainder term left at the end of the division

What is meant by a quadratic divisor?

• Polynomial division usually involves dividing by a linear term
  • a term of the form  where  is a constant and usually an integer
• It is possible to divide a polynomial by a quadratic term (and cubic, etc)
  • this would be a term of the form where and  are constants
  • this is what is meant by a quadratic divisor

How do I divide by a quadratic divisor?

• The process is the same as for a linear divisor
  • However, as  will not divide into  (in the polynomial division sense at least) the remainder, if there is one, could be of linear form, i.e.  where  and  are constants
    • It is possible that  and so the remainder is still a constant