Cambridge IGCSE Additional Mathematics · Syllabus 0606 · Factors of Polynomials
Factor Theorem
What is Factor Theorem?
A result stating that x - a is a factor of the polynomial P(x) if and only if P(a) = 0. It is the special case of the remainder theorem in which the remainder is zero, so the division leaves nothing over and P(x) can be written as x - a multiplied by another polynomial. The equivalence runs both ways: a zero value proves a factor, and a factor forces the value to be zero, so a non-zero value disproves the factor outright.
This definition is part of the Factors of Polynomials chapter in Cambridge IGCSE Additional Mathematics.