Polynomial function

Definition

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. It can be written in the form $f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0$ where $a_n, a_{n-1}, ..., a_1, a_0$ are constants.

5 Must Know Facts For Your Next Test

1. A polynomial function's degree is the highest power of the variable in the polynomial.
2. The leading coefficient is the coefficient of the term with the highest degree.
3. Polynomial functions are continuous and smooth curves.
4. The roots or zeros of a polynomial function are the values of $x$ for which $f(x) = 0$.
5. The Fundamental Theorem of Algebra states that every non-zero single-variable polynomial with complex coefficients has at least one complex root.

Review Questions

• What is the degree of the polynomial $f(x) = 3x^4 - 2x^3 + x - 7$?
• How do you find the roots of a polynomial function?
• What does the leading coefficient tell you about a polynomial function?

Related terms

Degree of Polynomial: The highest power of the variable in a polynomial.

Leading Coefficient: The coefficient of the term with the highest degree in a polynomial.

Fundamental Theorem of Algebra: A theorem stating that every non-zero single-variable polynomial with complex coefficients has at least one complex root.