Math Homework. Do It Faster, Learn It Better.

Monomials, Binomials, Polynomials

A monomial is any product of numbers and variables, like 17 , or 3 x y , or 4 x 2 , or

7 100 a 5 b 6 c 7 d 8 z 999

The only rules are that the variables should be raised to only positive integer powers (no square roots or 1 x 's allowed), and no plus or minus signs.

The coefficient of a monomial is the numerical part. For example, in the above examples, the coefficients are 17 , 3 , 4 and 7 10 .

A binomial is the sum of two monomials, for example x + 3 or 55 x 2 33 y 2 or

7 100 a 5 b 6 c 7 d 8 z 999 1 3 x

A trinomial is the sum of three monomials.

A polynomial is the sum of n monomials, for some whole number n . So monomials, binomials and trinomials are all special cases of polynomials. A polynomial can have as many terms as you want.

The degree of a monomial is the sum of the exponents of all its variables. The degree of a polynomial is the term of the polynomial that has the highest degree.