Concept of Polynomial
Definition :- The algebraic expression that is formed by
variable and constant, is known as Polynomial.
It may be of order one, two .three or so on
For Example X^2 + 4X +3 (One variable Polynomial)
Variable :- The variable are changing it’s value according
to the sum (Questions) or situation.
For example :- Months in a year
As soon as the year going the month changes like as Jan,
Feb, Mar, ….so on.
In this situation the month changes from Jan to Dec. So it
is called variable.
It may be x, y, z, a, b, c ……
Constant :- It is part of polynomial that never changes it’s
value according to situation or sum (Questions)
For example :- 1, 2, 3, 4, …..
In brief we can say all negative integers and whole numbers
are constant.
Types of polynomials
It may be categories in following types
1. Polynomial of one Variable :- In this only one variable
take place in algebraic expression. Like x or y or z…. so on
For Example 4X^2 + 5X
+7 (In this only x changes it’s value so it is polynomial of one
variable)
2. Polynomial of two Variable :- In this two variable take
place in algebraic expression. It is a combination of two variables like as (x
and y) or (y and z) or (z and x)
For examples :- (X^2) * Y + 4 * X * (Y^2) -7 (In
this only x and y changes it’s value so it is polynomial of two variable)
3. Polynomial of multi Variable :- In this more than two
variable take place in algebraic expression. It is a combination of more than
two variables like as (x, y, z) or (x, y, t) or (z, x, t) … so on
For examples :- (X^2) + (Y^2) = t^2 (In this only x, y, t changes it’s value so it
is polynomial of multi variable)
For Example 1, 2, 3, 4, … (In this no changes in values so it is constant polynomial )
Note 1 :- According to the syllabus of class 9th we
will discussing only about ‘Polynomial of one variable’
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Degree of Polynomial :-
The highest power of any algebraic expressions is known as
Degree of polynomial.
For example (4X^2 +
5X +7)
In this given expression the highest power of variable x is
2, so the degree of this polynomial is 2.
Note 2 :- If we are talking about constant polynomial so in
this case degree of this polynomial is 0.
According to degree of polynomial it can be categories in
following types :-
1. Linear polynomial :- The polynomial having highest power
of one, known as ‘Linear polynomial’
For example :- x + 3, y + 7
2. Quadratic polynomial :- The polynomial having highest
power of two, known as ‘Quadratic polynomial’
For example :- x^2 + x + 3, y^2 + y + 7
3. Cubic polynomial :- The polynomial having highest power
of three, known as ‘Cubic polynomial’
For example :- x^3 + x^2 + x + 3, y^3 + y^2 + y + 7
Coefficient of variable
The multiple of variable (x, x^2, X^3.. ) is known as ‘Coefficient of variable’
Note 3 :- If any expression is a factor of any polynomial it
happens only when
* When expression
satisfying the polynomial (Means reminder should be Zero)
* If reminder is not Zero so expression is not a factor of
polynomial.
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