Remainder Theorem

A student will likely to see this topic when they learn about the polynomial in secondary O-level a-maths class.

Useful Notes:

  • When a polynomial, g(x) is divided by a linear factor, (x-b), where b is equal to number. It will results a quotient q(x) with possible a reminder of r(x).
  • The relationship between f(x), linear factor, quotient and the remainder can be written as follow.

g(x) = Quotient * (1/Linear Factor) + Remainder

  • Since dividing g(x) by (x-b) will results a remainder of r(x). Thus,

g(b) = Remainder

  • If g(b) = 0, then x-b is a factor of the function (factor theorem).



What is the remainder of the function f(x) = 5+ 2×2 + 2x  when it is divided by the following linear factor?

  1. x – 1
  2. 1 – 3x
  3. x + 1


  1. 9
  2. 53/9
  3. 5

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