Degree

Definition

The degree of a polynomial function is the highest power of the variable in the expression. It determines the general shape and behavior of the graph.

5 Must Know Facts For Your Next Test

1. The degree indicates the maximum number of roots (real or complex) that a polynomial can have.
2. A polynomial's end behavior is determined by its degree and the leading coefficient.
3. Polynomials with even degrees tend to have similar end behaviors at both ends, either both up or both down.
4. Polynomials with odd degrees tend to have opposite end behaviors at each end, one up and one down.
5. The Fundamental Theorem of Algebra states that a polynomial will have as many roots as its degree, counting multiplicities.

Review Questions

• What is the degree of the polynomial $3x^4 - 2x^3 + x - 7$?
• How does the degree of a polynomial affect its end behavior?
• If a polynomial has a degree of 5, how many roots can it have?

Related terms

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

End Behavior: The direction in which the graph of a function moves as $x$ approaches positive or negative infinity.

Root: A solution to the equation $f(x) = 0$ where $f(x)$ is a function.