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.

The Remainder Theorem Rule to remember: If a polynomial [latex]f(x)[/latex] is divided by [latex](ax-b)[/latex] then the remainder is [latex]{f \left( \dfrac{b}{a} \right )}[/latex]. In the video tutorial I demonstrate this. Finding the remainder when a cubic polynomial is divided by x+1 In the vide

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)
The Remainder Theorem Rule to remember: If a polynomial [latex]f(x)[/latex] is divided by [latex](ax-b)[/latex] then the remainder is [latex]{f \left( \dfrac{b}{a} \right )}[/latex]. In the video tutorial I demonstrate this. Finding the remainder when a cubic polynomial is divided by x+1 In the vide

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)
The Remainder Theorem Rule to remember: If a polynomial [latex]f(x)[/latex] is divided by [latex](ax-b)[/latex] then the remainder is [latex]{f \left( \dfrac{b}{a} \right )}[/latex]. In the video tutorial I demonstrate this. Finding the remainder when a cubic polynomial is divided by x+1 In the vide

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.
The Remainder Theorem Rule to remember: If a polynomial [latex]f(x)[/latex] is divided by [latex](ax-b)[/latex] then the remainder is [latex]{f \left( \dfrac{b}{a} \right )}[/latex]. In the video tutorial I demonstrate this. Finding the remainder when a cubic polynomial is divided by x+1 In the vide