Algebra - Remainder Theorem

If a polynomial P(x) is divided by x - a until the remainder R does not contain x, then R = P(a)

P(x) = (x-a)Q(x) + R

Where P(x) is the polynomial expression

(x-a) is the expression being divided into the polynomial

Q(x) is the Quotient (the result of the algebraic division)

R is the remainder (of the algebraic division)

This can be used to:

• Find the remainder of a polynomial equation, given knowledge of P(x) and (x-a).
• Given knowledge of the remainder of a polynomial equation, it can be used to determine the term where polynomial is x⁰

Example

Where there is no remainder, this can be used (as factor theorem) to determine the factors of a polynomial expression.