Types of Polynomials: Monomials, Binomials, Trinomials, and More

Types of Polynomials

Polynomials are algebraic expressions that consist of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (not by a variable). Polynomials can be classified based on their degree and the number of terms.

The degree of a polynomial is the highest power of its variable, and it determines the shape and behavior of the polynomial's graph. The degree of a polynomial can be zero, one, two, three, or higher. The degree of a polynomial is indicated by the highest exponent of the variable in a monomial within the polynomial. For example, in the polynomial P(x) = 6x^4 + 3x^2 + 5x + 19, the degree of the polynomial is 4, as the highest power of the variable is 4.

Terms of a Polynomial

The terms of a polynomial are the parts of the expression that are generally separated by "+" or "-" signs. The classification of a polynomial is done based on the number of terms in it.

Types of Polynomials

Monomial

A polynomial containing one non-zero term is called a monomial. For example, 8x^5 and -7y^3 are both examples of monomials.

Binomial

A polynomial containing two non-zero terms is called a binomial. For example, 7x^6 - 3x^4 and 5x^4 + 3x^2 are both examples of binomials.

Trinomial

A polynomial containing three non-zero terms is called a trinomial. For example, 5x^4 + 3x^2 - 8 and 7x^5 - 3x^2 + 9x are both examples of trinomials.

Polynomial containing 4 terms (Quadronomial)

A polynomial containing four terms is called a quadronomial. For example, 7x^5 - 3x^2 + 9x + 5 and 2x^6 + 8x^3 - 7x^2 + 9x are both examples of quadronomials.

Polynomial containing 5 terms (Quintrinomial)

A polynomial containing five terms is called a quintrinomial. For example, y^6 + 8y^5 + 9y^4 + 9y^2 + 7 is an example of a quintrinomial.

Polynomials based on degree

Polynomials can also be classified based on their degree, such as:

• Zero polynomial: A polynomial with zero degree, like 0.
• Constant polynomial: A polynomial with only a constant term, like 5.
• Linear polynomial: A polynomial with degree one, like x + 4.
• Quadratic polynomial: A polynomial with degree two, like x^2 + 2x + 3.
• Cubic polynomial: A polynomial with degree three, like x^3 + 3x - 5.
• Quartic polynomial: A polynomial with degree four, like x^4 + 3x^3 + 3x^2 + 2x + 1.
• Quintic polynomial: A polynomial with degree five, like x^5 + 6x^4 + 4x^3 + 3x^2 + 2x + 1.
• Sextic polynomial: A polynomial with degree six, like x^6 + 7x^5 + 6x^4 + 5x^3 + 4x^2 + 3x + 2.

Polynomials can have any number of terms, but not an infinite number. The word "polynomial" is derived from the Greek words "poly" meaning "many" and "nomial" meaning "terms," so altogether it is said as "many terms."