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 the following
A) 9x^{2} + 8x + 2
B) 7x^{2} + 6x + 2
C) 9y^{2} + 8x + 3
D) 7y^{2} + 6x + 3
E) 6y^{2} + 5x + 2
F) 2x^{3} + 3y^{2} + 2x |
Check whether the below are polynomials or not
A) 55
B) 300
C) 2y^{-3}
D) 5y^{-3} + 2x + 1
E) x + 2/x
F) y + 3/y
G) 3x^{2} + 2x + 2
H) 4x^{2} + 4x + 3 |
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