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
- The degree indicates the maximum number of roots (real or complex) that a polynomial can have.
- A polynomial's end behavior is determined by its degree and the leading coefficient.
- Polynomials with even degrees tend to have similar end behaviors at both ends, either both up or both down.
- Polynomials with odd degrees tend to have opposite end behaviors at each end, one up and one down.
- 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?
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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.
