Types of Polynomial On the Basis of Number of Terms

In mathematics, a polynomial is an algebraic expression consisting of variables and coefficients. These expressions are typically used in equations to solve for unknown variables.

The degree of a polynomial is the highest exponent of the variable in the expression. For example, in the equation x²+4x+3, the degree would be 2 because x is raised to the second power.

The coefficients are the numerical factors in front of each variable. In our example equation, the coefficient are 1, 4, and 3.

The concept of a polynomial is studied under the branch of algebra. Before we get into the definition of a polynomial and its various types, let’s review the basic terms that make up a polynomial.

Definition of polynomial

A polynomial is an algebraic expression in which the variables have non-negative integer powers.

For example

3x² + 5

4x² + 9x + 1

Types of Polynomial

There are several different types of polynomials, which are determined by both the degree of the polynomial and the number of terms involved.

Types of polynomial on the basis of number of terms

Polynomials are classified and named according to how many terms it has. In general, the type of polynomial is named by putting the words mono, bi, and tri in front of “nomial”.

When we talk about mono, we’re referring to one. Bi refers to two, and tri indicates three. The corresponding types are monomial, binomial, and trinomial.

Monomial

A polynomial is a mathematical expression that contains one or more terms. A polynomial with only one non-zero term is called a monomial.

Example:

3x⁵ in this polynomial, there is only one none zero term i.e.3x⁵ Therefore, it is an example of a monomial.

Binomial

A polynomial is a mathematical expression that contains one or more algebraic terms. These terms are connected by coefficients, which are numerical values that multiply the algebraic terms. A binomial is a polynomial that contains only two algebraic terms.

For example:

2x⁴-3x³

In this polynomial, there are two non-zero terms i.e. 2x⁴ and 3x³. Therefore, it is an example of a binomial.

Trinomial

A polynomial is a mathematical expression containing one or more terms, including at least one non-zero term. A trinomial is a specific type of polynomial that contains three non-zero terms.
For example:

2x³-x²-8 Here we have three non-zero terms i.e. 2x³, -x² and-8. Therefore, it is an example of a trinomial.

Quadrinomial Polynomial

A polynomial containing four terms is called a quadrinomial polynomial.

For example 4x⁴-3x³+2x+5

Quintrinomial polynomial

A polynomial containing five terms is called a quintrinomial polynomial.

For example:

X⁶+2x⁵+3x⁴+x²-7

Types of polynomial on the Base of Degree of a Polynomial

There are different types of polynomials based on their degree. The degree of a polynomial is determined by the highest power of the variable in the equation. For example, if the highest power of the variable in an equation is 2, then the degree of that polynomial is 2. Here are the different types of polynomials based on their degree:   Linear polynomials. Quadratic polynomials. Cubic polynomials have. Biquadratic polynomial Higher order polynomials have a degree greater than 4.

What is Linear Polynomial?

A linear polynomial is a polynomial that has a degree of 1. An example of a linear polynomial is x + 2. The general form of a linear polynomial is ax + b, where a and b are constants.

What is a quadratic polynomial?

A quadratic polynomial is a polynomial of degree two. The general form of a quadratic polynomial is ax^2 + bx + c Where a, b, and c are constants. An example of a quadratic polynomial would be: 3x^2 + 5x – 2

What is cubic Polynomial?

A polynomial whose degree is 3 is called a cubic polynomial. Cubic polynomial in variable x can be in general form of ax³+bx²+cx+d=0

For example: 2x³+5x²-2x-4

What is a biquadratic polynomial?

A polynomial of degree 4 is called a biquadratic polynomial. Biquadratic polynomial in variable x can be in general form of ax⁴+bx³+cx²+dx+e=0 For example: 5x⁴-2x³+2x²+4x-5

What is a constant Polynomial?

A constant polynomial is a polynomial in which all variables have a power of zero. In other words, a constant polynomial is simply a number. An example of a constant polynomial would be:   4x^0 + 2x^0 + 5x^0= 11

What is zero Polynomial?

A zero polynomial is a polynomial with all coefficients equal to zero. The degree of zero polynomial is not defined.