Classification of polynomial according to the number of terms?

Answer 1

Polynomials can be classified based on the number of terms they contain. A polynomial with one term is called a monomial, such as 5x or -2y^2. A polynomial with two terms is called a binomial, like 3x + 2 or 4y - 7. A polynomial with three terms is called a trinomial, for example, 2x^2 + 5x - 3. Polynomials with more than three terms are simply referred to as polynomials.

Answer 2

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.

Answer 3

Quadratic