Algebra Maths

Basic Concepts of Polynomial: Monomial, Binomial, Trinomial and Polynomial

Maths - BASIC CONCEPTS OF POLYNOMIAL: MONOMIAL,BINOMIAL, TRINOMIAL AND POLYNOMIAL
Written by Mary Christina

Monomial:

An Algebraic expression that contains only one term is called a monomial.
Example: 2x³, 8xy, -5c, -2, etc

Binomial:

An Algebraic expression that contains only two terms is called a binomial.
Example: 2x-3y, l²-m², 2-3y²z, a+b, etc

Trinomial:

An Algebraic expression that contains only three terms is called a trinomial.
Example: x+y+z, 3a²-b²-c, l²m-m²n-n, 3x³-2y²-z,etc

How do you remember the names?

Think about cycles!

Basic Concepts of Polynomial: Monomial, Binomial, Trinomial and Polynomial

Polynomial:

An algebraic expression that contain finite number of terms with non- zero coefficients is called a polynomial. In other words it is an expression that contains finite number number of terms with combination of variables, whole number exponents of variables and constants.
Example: a+b+c+d, 7xy, 2x-3y-z, 3x⁵;+4x⁴-5x³-6x²+3x-5,etc

Degree of a Polynomial:

The monomials in the polynomials are called the terms. The highest power of the terms is the degree of the polynomial.

The coefficient of the highest power of x in a polynomial is called the Leading Coefficient of the polynomial.
Example: 2x⁵-x⁴+7x³-6x²+12x-4 is a polynomial in x.

Here we have six monomials 2x⁵, -x⁴, 7x³, -6x², 12x and -4 which are called the terms of the polynomial.
Degree of the polynomial is 5.

The Leading Coefficient of the polynomial is 2.

Like terms and Unlike terms:

Like terms contain the same variables having same powers.
Unlike terms contain different variables having different powers.

Consider the following Expression:

2x²+3x-4 All are unlike terms.
2a²-3a² These are like terms.

Look at the following expression:

3x, 5x², 2xy, -70x, -7, -3y², -3x², -20yx, 20, 4x, 3y

We Can list out the Like terms as:

  1. 3x, -70x and 4x
  2. 5x² and -3x²
  3. 2xy and -20yx
  4. -7 and 20.

About the author

Mary Christina

Mary Christina from Chennai, India. She has completed Master Degree in Mathematics and she loves to teach and share about her knowledge in maths for High School and College Students...