Polynomials

A polynomial in one variable $x$ is an expression of the form $a_n x^n + a_{n-1} x^{n-1} + \\dots + a_1 x + a_0$, where $n$ is a non-negative integer and the coefficients $a_i$ are real (or sometimes integer or rational) numbers. The degree of the polynomial is the highest power of $x$ with a nonzero coefficient.

Important properties

• The sum, difference, and product of two polynomials is a polynomial.

• Polynomials can be evaluated by substituting values for the variable.

• Polynomials can be factored into products of lower-degree polynomials, sometimes involving irreducible polynomials.

• The degree of the sum or difference of two polynomials is at most the highest degree present.

• The degree of the product of two polynomials is the sum of their degrees.