Remainder theorem
Remainder theorem
You may want to refresh your memory on polynomial long division and synthetic division to better understand this lesson. The remainder theorem simply states that if a polynomial f(x) is divided by a linear expression xr, the value of f(r) is equal to the remainder.
Basic concepts:
 Polynomial long division
 Polynomial synthetic division
Related concepts:
 Integration of rational functions by partial fractions
Lessons
Notes:
$\cdot$ When a polynomial, $P(x)$, is divided by $(xa)$: Remainder $=P(a)$
$\cdot$ When a polynomial, $P(x)$, is divided by $(axb)$: Remainder $=P(\frac{b}{a})$

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 $\left( {2x  5} \right)$