What is a polynomial?
- A polynomial is an algebraic expression consisting of a finite number of terms, with non-negative integer indices only
What is polynomial division?
- Polynomial division is a method for splitting polynomials into factor pairs (with or without an accompanying remainder term)
- 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:
- 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
- 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