Remainder theorem

Lessons

1. Understanding the remainder Theorem
   Prove the Remainder Theorem
   
2. Finding the Remainder Using Synthetic Division and the Remainder Theorem
   Find the remainder when $\left( {4{x^3} - 7x + 10} \right)$ is divided by $\left( {2x - 5} \right)$
   1. Using synthetic division
   2. Using the remainder theorem
3. When $\left( {8{x^3} + a{x^2} + bx - 1} \right)$ is divided by:
   i) $\left( {2x - 5} \right)$, the remainder is $54$
   ii) $\left( {x + 1} \right)$, the remainder is $- 30$
   Find the values of $a$ and $b$.