The Remainder Theorem

Rule to remember:

  • If a polynomial f(x) is divided by (ax-b) then the remainder is {f \left( \dfrac{b}{a} \right )}.

In the video tutorial I demonstrate this.

Finding the remainder when a cubic polynomial is divided by x+1

In the videos that follow, I run through some typical remainder theorem questions that you are likely to encounter. I start with this example.

Example in the video

  1. Find the remainder when {x^3} - 4{x^2} + 2x - 3 is divided by (x+1)

Finding the remainder when a quartic polynomial is divided by 2x-1

Example in the video

  1. Find the remainder when  4{x^4} - {x^2} - 8x + 6  is divided by (2x - 1)

Finding constants in a polynomial given the remainders

Example in the video

  1. When {x^3} + a{x^2} + bx - 1 is divided by (x-1) the remainder is 3 and when divided by (x+2) the remainder is -27. Find a and b.