Before you understand this topic you should read 
What is Algebraic Expression ?
What are Terms ?
An algebraic Expression with one or more terms is called Polynomials .
Eg. 2a, 5x + y, 2x2 + 3x + y, all are polynomials
If the variable in the polynomial is x, we may denote the polynomial by p(x) or q(x) or r(x)… etc
For example:
Polynomial 5x^{3} + 3x^{2} + x can be written as:
p(x) = 5x^{3} + 3x^{2} + x
Polynomial a^{3} + 2a + 3 can be written as:
q(a) = a^{3} + 2a + 3
Polynomial r^{2} + r + 35 can be written as:
f(r) = r^{2} + r + 35
A polynomial can have any number of terms.
Polynomials can be of following types:
Zero Polynomial
Monomial
Binomial
Trinomial
(You can study these types from the above provided link)
Have a look at the below expression and study what are terms, constant term, variables, power and coefficients of Polynomial.
3x^{2} + 2x + 2
Terms in given Polynomial are : 3x^{2} + 2x + 2
Constant Term in given Polynomial is : 3x^{2} + 2x + 2
Variables in given Polynomial are : 3x^{2} + 2x + 2
Power / Exponent in given Polynomial is : 3x^{2} + 2x + 2
Coefficients in given Polynomial are : 3x^{2} + 2x + 2
Note: If Power or Exponent is negative then it is not a polynomial . For example x^{2} or 2x^{2}
Let's study few examples and find terms, constant term, variables, power and coefficients of Polynomial
Example  1 : Find terms, constant term, variables, power and coefficients from 4y^{2} + 5x + 3
Solution : The given Polynomial is 4y^{2} + 5x + 3 so
Terms in given Polynomial are : 4y^{2} + 5x + 3
Constant Term in given Polynomial is : 4y^{2} + 5x + 3
Variables in given Polynomial are :4y^{2} + 5x + 3
Power in given Polynomial is : 4y^{2} + 5x + 3
Coefficient in given Polynomial are : 4y^{2} + 5x + 3
Example  2 : Find terms, constant term, variables, power and coefficients from 5y^{2} + 6x  4
Solution : The given Polynomial is 5y^{2} + 6x  4 so
Terms in given Polynomial are : 5y^{2} + 6x  4
Constant Term in given Polynomial is : 5y^{2} + 6x  4
Variables in given Polynomial are : 5y^{2} + 6x  4
Power in given Polynomial is : 5y^{2} + 6x  4
Coefficient in given Polynomial are : 5y^{2} + 6x  4
Example  3 : Find terms, variables, power and coefficients from 5x^{3} + 4y^{2} + 3x
Solution : The given Polynomial is 5x^{3} + 4y^{2} + 3x so
Terms in given Polynomial are : 5x^{3} + 4y^{2} + 3x
Variables in given Polynomial are : 5x^{3} + 4y^{2} + 3x
Powers in given Polynomial are : 5x^{3} + 4y^{2} + 3x
Coefficients in given Polynomial are : 5x^{3} + 4y^{2} + 3x
Example  4 : Is 25 a polynomial
Solution  Yes 25 is a polynomial as one term is allowed in polynomial and this 25 is also a constant
Example  5 : Is x^{3} is polynomial
Solution : No, x^{3} is not a polynomial because its power is negative

Study More Solved Questions / Examples
Find terms, constant term, variables, power and coefficients from 9x^{2} + 8x + 2 
Find terms, constant term, variables, power and coefficients from 7x^{2} + 6x + 2 
Find terms, constant term, variables, power and coefficients from 9y^{2} + 8x + 3 
Find terms, constant term, variables, power and coefficients from 7y^{2} + 6x + 3 
Find terms, constant term, variables, power and coefficients from 6y^{2} + 5x + 2 
Find terms, variables, power and coefficients from 2x^{3} + 3y^{2} + 2x 
Is 55 a polynomial 
Is 300 a polynomial 
Is 2y^{3} is a polynomial 
Is 5y^{3} + 2x + 1 is a polynomial 
Is this expression is polynomial x +  2 x 

Is this expression is polynomial y +  3 y 

Is 3x^{2} + 2x + 2 is a polynomial 
Is 4x^{2} + 4x + 3 is a polynomial 
