degree of a polynomial

The degree of a polynomial is its highest power — the tallest tower among all its terms. If you look at 4x^3 - x + 6, the powers are 3, 1, and 0, so the degree is 3. The degree tells you, at a glance, how complicated and how curvy the polynomial is.

To find it, write down the degree of each term (for one variable, that is just its exponent) and take the largest. For a term with several variables, like 2x^2y^3, you add the exponents: 2 + 3 = 5. The degree of the whole polynomial is the maximum of those term-degrees.

Degree controls behavior: degree 1 is a line, degree 2 is a parabola, degree 3 a cubic, and so on. A nonzero constant like 7 has degree 0. The zero polynomial (just 0) is a special case — its degree is usually left undefined, since it has no nonzero term to measure.