In the context of polynomial equations, the term “least degree” refers to the smallest exponent of the variable in the polynomial expression when it is expressed in its standard form. A polynomial is typically written as a sum of terms, each consisting of a coefficient and a variable raised to a non-negative integer exponent. The degree of a polynomial is determined by the highest exponent present. However, the least degree focuses on the lowest exponent that appears in the polynomial.
For example, consider the polynomial f(x) = 2x^4 – 3x^3 + x – 7. The degrees of the terms are 4, 3, 1, and 0. Thus, the least degree of this polynomial is 0, corresponding to the constant term (-7).
Understanding the least degree is essential because it helps identify the behavior of the polynomial at certain values, the number of roots, and the overall characteristics of the polynomial function.