Polynomials: An algebraic expression is an expression which is made up of variables and constants along with some algebraic operations. The several parts of an algebraic expression seperated by + or – operations are called the terms of the expression. e.g.
(i) is an algebraic expression with three terms and three variables
(ii) is an algebraic expression with three terms and two variables
(iii) is an algebraic expression with two terms and one variable
(iv) is an algebraic expression with one terms and one variable.
In an algebraic expression , if the powers of variables are non-negative integers , then it is a polynomial.
In the above examples , (i) and (ii) are polynomials, where as (iii) and (iv) are not polynomials.
Polynomials in one variable :
Polynomials in one variable are algebraic expressions that consists of terms in the form of
Each term of a polynomial has a coefficient . so in
Degree of a polynomial:
The degree of a polynomial in a single variable is the highest power of
In general any polynomial of degree is an expression of the form
In particular if all the constants are zero , then we get , the zero polynomial. Zero polynomial has no non-zero terms so the degree of zero polynomial is not defined.
A polynomial containing only the constant term is called constant polynomial. e.g.
Let is a non-zero constant polynomial ,
Therefore the degree of any non-zero constant polynomial is zero.
Based on the number of terms, polynomials are classified as
(i) A polynomial containing one term is called a monomial. e.g. etc. all are monomials.
(ii) A polynomial containing two terms is called a binomial. e.g.
(iii)A polynomial containing three terms is called a trinomial. e.g. etc. all are trinomials.
Linear polynomial :
A polynomial of degree one is called a linear polynomial. A linear polynomial in
Any linear polynomials in
Quadratic polynomial :
A polynomial of degree 2 is called a quadratic polynomial. A quadratic polynomial in one variable will have at most tree terms. Any quadratic polynomial in
Cubic polynomial :
A polynomial of degree 3 is called cubic polynomials. Any cubic polynomial can have at most 4 terms. all are examples of cubic polynomials.
Also Read :
- Factoring Polynomials Formula and Factoring Polynomials Worksheet with Answers
- Factoring trinomials worksheet