Remainder theorem  Polynomial Functions
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 $\left( {2x  5} \right)$