Degree

Definition

The degree of a polynomial is the highest power of the variable in its expression. It determines the most significant term when expanding or simplifying the polynomial.

5 Must Know Facts For Your Next Test

1. The degree of a non-zero constant polynomial is 0.
2. The degree of a zero polynomial is undefined or sometimes considered as negative infinity.
3. In a polynomial function, the degree dictates the maximum number of roots and turning points.
4. A polynomial with degree n may have up to n-1 turning points.
5. The leading coefficient is associated with the term having the highest degree.

Review Questions

• What is the degree of the polynomial $3x^4 + 2x^3 - x + 7$?
• If a polynomial has a degree of 3, how many turning points can it have at most?
• Why is the degree important when analyzing polynomial functions?

Related terms

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

Root: A value for which a given function equals zero.

Turning Point: A point where a graph changes direction from increasing to decreasing or vice versa.