Cambridge O Level Additional Mathematics · Syllabus 4037 · Factors of Polynomials
Complete Factorisation
What is Complete Factorisation?
The expression of a polynomial as a product of factors that cannot be broken down further into brackets with integer coefficients. For a cubic this means either three linear factors, or one linear factor multiplied by a quadratic factor that does not factorise, because its discriminant is either negative or positive but not a perfect square. It is reached by using the factor theorem to find one linear factor, dividing it out to obtain a quadratic, and then factorising that quadratic if it factorises. A factorisation that stops at a linear factor times a quadratic that could still be factorised is incomplete.
This definition is part of the Factors of Polynomials chapter in Cambridge O Level Additional Mathematics.