You may be required to manipulate polynomials including expanding brackets, simplifying expressions, factorising and polynomial division possibly with the use of remainder and factor theorem.
Expand and Simplify
Expand and simpify – this works in the same way as expanding double brackets but you should end up with 6 terms before simplification.
Factor theorem states that if a polynomial is divisible by then and vice versa.
Example – show that is divisible by x-2. The easiest way to do this is to use factor theorem which states that f(x) is divisible by x-2 if f(2)=0. , hence x-2 is a factor of f(x) and f(x) is divisible by x-2.
Remainder theorem states that if a polynomial is not divisible by then dividing by will result in a remainder in which case .
Example – find the remainder when is divided by x+1. The simplest way to do this is to use remainder theorem which states that the remainder when f(x) is divided by x+1 is f(-1). and so the remainder when f(x) is divided by x+1 is -6.