# Long Division of Polynomials

Example 1 Divide $x^3 + 3x^3 + 2x + 1$ by $x+2$. Example 2 Perform a long division: $(4x^4-6x^3+2x^2-3x+5) \div (2x+1)$.

# Polynomial Equations and Maximum Coefficients

If $\alpha$ is a root of a polynomial equation $P(x) = 0$, then $P(\alpha) = 0$, and if $M$ is the maximum coefficient value of $|a_{n}|, |a_{n-1}|, |a_{n-2}|, \cdots ,|a_2|, |a_1|$ then $nM \ge |a_{n}| + |a_{n-1}| + |a_{n-2}| + \cdots + |a_2| + |a_1|$. […]