Algebraic Division (Edexcel IGCSE Further Maths)

What is algebraic division?

• Algebraic division (or polynomial division) is a method for splitting polynomials into factor pairs (with or without an accompanying remainder term)
  • On the exam you will use it to factorise polynomials, or to help simplify algebraic fractions

• Remember that a polynomial is an algebraic expression consisting of
  • a finite number of terms
  • with non-negative integer indices only

 

How do I perform algebraic division?

• The method used for algebraic division is just like the method used to divide regular numbers
  • i.e. the long division method (sometimes called 'bus stop division')

• On your exam the polynomial you are dividing (known as the dividend) will normally be of degree 3 or 4
  • That is, with powers of x  up to x³ or x⁴
• The term you are dividing by (known as the divisor) will be a linear term
  • Usually in the form (x ± a)
  • But possibly in the form (ax ± b)
• The answer to an algebraic division question is built up term by term
  • Working downwards in powers of the variable (usually x)

• Start with the highest power term of the answer
  • Write out this multiplied by the divisor and subtract

•  Continue the process for each decreasing power term
  • multiplying by the divisor and subtracting each time

•  Continue until you are left only with a number (with no x's)
  • That number is the remainder
  • If the divisor is a factor of the polynomial, the remainder will be zero