Polynomial function

Definition

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. These functions are characterized by terms of the form $a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$, where $a_i$ are constants and $n$ is a non-negative integer.

5 Must Know Facts For Your Next Test

1. The degree of a polynomial function is the highest power of the variable in its expression.
2. Polynomial functions are continuous and smooth, meaning they have no breaks, holes, or sharp corners.
3. The end behavior of polynomial functions depends on the leading term (the term with the highest degree).
4. Polynomial functions can be classified by their degree: linear (degree 1), quadratic (degree 2), cubic (degree 3), etc.
5. The Fundamental Theorem of Algebra states that every non-zero polynomial function has at least one complex root.

Review Questions

• What determines the end behavior of a polynomial function?
• How do you classify polynomial functions based on their degree?
• What does the Fundamental Theorem of Algebra state about polynomial functions?

Related terms

Degree:

The highest power of the variable in a polynomial function.

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

Root:

A solution to the equation formed by setting the polynomial equal to zero.