Basic Definitions and Concepts
Contents
Definition
A polynomial is an algebraic expression in which the variables involving are having nonnegative integral powers.
Examples 2x³+5x+2, 8y³+5xy+x2 etc.
Ok, lets now define the term Algebraic Expressions, variables and constants.
Variables
A symbol (x,y,z,a,b,g,h etc.) that can be assigned different numerical values.
Example Area of a triangle = ½×base(b)×height(h), Here ‘b’ and ‘h’ can have different numerical values. So, ‘b’ and ‘h’ are variables.
Constants
Symbols having fixed numerical values are called constants.
For Example 2, 3, 1/2, 22/7, etc.
Algebraic Expressions
When we combine the variables and constants along with operations +, , ×, and ÷ (few or all), the result obtained is called an algebraic expression.
Example 2x³+5x+2,
Note This above expression contains 3 terms (Home Work Name these)
Coefficients
The numerical values associated with the variables in a polynomial are called coefficients. For example In the polynomial, 2x³+5x²+x+2 the coefficients of x³, x², x are 2, 5 and 1 respectively whereas 2 is the constant term.
Degree of a Polynomial

Degree of a Polynomial of one Variable
If a polynomial is in one variable, then the variable with highest nonnegative integral power is called its degree.
Ex x³+8x²+x+2. Here there are 4 terms namely x³, 8x², x, 2 and the variable with the highest power is x³. So the degree of the above polynomial is 3.

Degree of a Polynomial of two or more Variables
In this case, we add the powers of the variables in each term, and the highest sum obtained is called its degree.
Ex 8y³+5x²y²+x2.
Degree of this polynomial is 4 (2nd Term i.e., 5x²y² = Sum of powers 2+2)
Polynomials with various Degrees
 Linear Polynomial – Having degree 1. Ex x2
 Quadratic Polynomial Having degree 2. Ex y²+x2
 Cubic Polynomial Having degree 3. Ex 8y³+5x²+x
 Biquadratic Polynomial Having degree 4. Ex 8y³+5x²y²+x2
Constant Polynomial
A polynomial containing only one term, i.e, a constant term is called a constant polynomial. Its degree is zero.
Ex 2, 1/8 etc.
Zero Polynomial
A polynomial containing only one term, i.e, zero is called a zero polynomial. Its degree is not defined.