Polynomial Division (OCR AS Maths: Pure)

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Polynomial Division

What is a polynomial?

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

2.5.2 Polynomial not polynomial, Edexcel A Level Maths: Pure revision notes 

What is polynomial division?

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

2.5.2 Polynomial Division What Is, Edexcel A Level Maths: Pure revision notes

  • At A level you will most frequently use it to factorise polynomials, or when dealing with improper (ie 'top-heavy') algebraic fractions

How do I divide polynomials?

  • The method used for polynomial division is just like the long division method (sometimes called 'bus stop division') used to divide regular numbers:

2.5.2 Bus Stop Div, Edexcel A Level Maths: Pure revision notes

  • At A level you will normally be dividing a polynomial dividend of degree 3 or 4 by a divisor in the form (x ± p)
  • The answer to a polynomial division question is built up term by term, working downwards in powers of the variable (usually x)

  • Start by dividing by the highest power term
  • Write out this multiplied by the divisor and subtract

2.5.2 Polynomial Division Illustration_1, Edexcel A Level Maths: Pure revision notes

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

2.5.2 Polynomial Division Illustration_2, Edexcel A Level Maths: Pure revision notes

  •  Continue until you are left with zero

2.5.2 Polynomial Division Illustration_3, Edexcel A Level Maths: Pure revision notes

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

Worked example

2.5.2 Polynomial Division Example, Edexcel A Level Maths: Pure revision notes

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Roger

Author: Roger

Expertise: Maths

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.