Algebraic Division (Edexcel IGCSE Further Maths)

Spec point — 3A

Algebraic Division

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

Exam Hint

• Don't rush when doing algebraic division

  • Finding and fixing a mistake can take longer than taking the time to do it right the first time!

• Before starting algebraic division make sure it is really necessary

  • For example, if all you need is the remainder then using the remainder theorem would be quicker

Worked Example