Of the many different types of polynomials, the three most common are monomials, binomials and trinomials. Within these three common types are more specific types of polynomials such as quadratics and linear functions. Polynomial types that do not fit into the most common types are listed under the degree of the polynomial.
Monomials are polynomials with only one term such as 3x^2, 4x^5, 3 and -2x. A constant polynomial is a specific monomial polynomial function and includes functions such as 3, 10, 2 and -4. Monomials that have 1 as the highest exponent, such as 3x and 12x, are part of a specific type of polynomial called linear polynomial functions. If the monomial has 2 as the highest exponent, then it belongs to the specific type called a quadratic polynomial function. Monomials belonging to the quadratic subgroup include functions such as x^2 and 4x^2.
A polynomial with two terms is of the binomial type. Examples of binomials include 3x+2, 4x^4-3, 7x^9+x^3 and x^2-4x^7. Binomial polynomials that have 1 as the highest exponent in the function are part of a specific type called linear polynomials. Linear polynomials that belong in the binomial group include functions such as 3x-6, 3-x, 12x+6 and 3-2x. If the binomial has 2 as the highest exponent, then it, too, is part of a specific type called a quadratic. Quadratic binomials include functions such as 5x^2+4 and 3x^2-5x.
An example of a trinomial, 4x^4+3x^2+7 is a polynomial function with three terms. Like the other types of polynomials, the exponents are all whole numbers and do not necessarily need to be in order numerically. In the trinomial example, the exponents are 4, 2 and 0. The exponents for a trinomial do not have to be 2, 1 and 0.
Degree of a Polynomial
Polynomials that do not fit into the three common types are placed into types according to the degree of the polynomial. The degree of the polynomial is determined by highest exponent the function has. For example, the polynomial function, x^9+4x^8-3x^2-9, is a polynomial of degree 9 since the highest exponent the function has is x^9. In this category, there are endless types of polynomials since the degree of a polynomial can go as high as infinity.
Exponents and Variables
For the common types of polynomials, the exponents can be any positive whole number. A monomial's exponent is not limited to 0, but can be any number such as 7, 12 or 8. The monomial can also have any number of variables as long as it only has one term. The same applies for binomials and trinomials as long as the functions have two and three terms, respectively.