**Polynomial**
A

**polynomial** is an algebraic expression of the form

$ax^n + bx^{n-1} + \cdots + rx + s$

where $a, b, \dots r$ and $s$ are constants, called the

**coefficients** of the polynomial. The largest exponent of $x$ appearing in the expression with a nonzero coefficient is called the

**degree** of the polynomial.

**
Examples **
$3x-2$ \gap[10] has degree 1, as the highest power of $x$ that appears with a nonzero coefficient is $x = x^1.$ Degree 1 polynomials are called **linear expressions.**
\\
\\ $2x - x^2$ \gap[10] has degree 2, as the highest power of $x$ that appears with a nonzero coefficient is $x^2.$ Degree 2 polynomials are called **quadratics.** \\
\\ $0x^4+3x^2+1$ \gap[10] also has degree 2, as the highest power of $x$ that appears with a *nonzero* coefficient is $x^2.$
\\
\\ $4x^3-x^2-5$ \gap[10] has degree 3. Degree 3 polynomials are called **cubics.**
\\
\\ $x^4-1$ \gap[10] has degree 4. Degree 4 polynomials are called **cuartics.**