Remainder theorem

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Understanding the remainder Theorem
Prove the Remainder Theorem
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
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 $b$ .