What is the term for the highest power in an algebraic expression?

The highest power in an algebraic expression is referred to as the degree of the polynomial. The degree indicates the highest exponent attached to any variable in the expression. For instance, in the expression 4x^3 + 2x^2 - x + 5, the term with the highest exponent is x^3, which makes the degree of this polynomial equal to 3. Understanding the degree is important in determining the overall behavior of the polynomial, such as how it behaves as the values of the variables increase or decrease, and it also plays a critical role in polynomial classification, such as identifying whether it is a linear, quadratic, cubic, etc.

The other terms—coefficient, term, and variable—play different roles within the algebraic expression but do not refer specifically to the highest power. A coefficient is a numerical factor in front of a variable, a term refers to each part of the expression that is added or subtracted, and a variable represents an unknown quantity usually denoted by letters.