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.
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\\ $2x - x^2$ \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 $x^2.$
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\\ $4x^3-x^2-5$ \gap[10] has degree 3. Degree 3 polynomials are called cubics.
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\\ $x^4-1$ \gap[10] has degree 4. Degree 4 polynomials are called cuartics.