A polynomial expression is an algebraic expression that involves only addition, subtraction, multiplication of non-negative integer powers of some variable or variables. For instance
\begin{equation*}
2x^3-4x^2-2x+4
\end{equation*}
is a polynomial in a single variable \(x\text{.}\) The expression
\begin{equation*}
4s^3 t^5 - s^2 t^3 + \sqrt{2} s t
\end{equation*}
is a polynomial in the two variables \(s\) and \(t\text{.}\) A polynomial consists of a number of terms that are being added. Each term has a coefficient, and in the case of a single variable, the exponent determines the degree of the term. For example, the terms of \(2x^3-4x^2-2x+4\) are
\(2x^3\) with a coefficient of \(2\) and degree \(3\) which we would call a cubic term.
\(-4x^2\) with a coefficient of \(-4\) and degree \(2\) which we would call a quadratic term.
\(-2x = -2x^1\) with a coefficient of \(-2\) and degree \(1\) which would be called a linear term.
\(4 = 4x^0\) is a constant term with a coefficient of \(4\) and degree \(0\text{.}\)
The term with the highest-degree is called the leading term of the polynomial. The coefficient of the leading term is the leading coefficient and its degree determines the degree of the polynomial. In our case, \(2x^3-4x^2-2x+1\) has leading term \(2x^3\) with leading coefficient \(2\) and degree \(3\text{.}\)
When adding or subtracting polynomials, combine like terms in the expression. These are terms with the same variables and degree, but possibly different coefficients. For instance, the following involve like terms of \(x^2\)
