Classification of polynomial according to the number of terms?

Strictly we do not classify polynomials by the number of terms but by the highest power of the variable (its degree).

For example, if x is the variable then a polynomial with highest power...

... x0 (degree 0) is a constant e.g. 4x0 = 4

... x1 (degree 1) is linear e.g. 2x1 + 5 = 2x + 5

... x2 (degree 2) is a quadratic e.g. 3x2 - 2x + 1

... x3 (degree 3) is a cubic e.g. 2x3 - 3x2 - 2x + 1

... x4 (degree 4) is a quartic e.g. 7x4 + 2x3 - 3x2 - 2x + 1

(degree 5) quintic, (degree 6) sextic, (degree 7) septic, (degree 8) octic,...

Although it appears as if the degree of a polynomial is always one less than the number of terms, in general this not the case. For example, x3 - 9 is cubic with only 2 terms or 4x8 is an octic with only one term.