Equations of the type
x ^{ 3 } − 3x ^{ 2 } + 4x + 10
are called polynomials.
Here,
x ^{ 3 } , −3x ^{ 2 } , 4x , 10 are called terms of polynomials.
A Polynomial has
- Variables like x, y with powers as whole numbers (0, 1, 2, 3, ....). If Power is not a whole number , the equation is not a polynomial.
- constants like 10
Polynomial in one variable
In this chapter,
We will be studying polynomials which are in one variable, i.e. only has x or y, but not both.
Example - x ^{ 2 } + 2x - 3 is a polynomial in one variable as there is only x
But x ^{ 2 } + 2y - 3x = 0 is not a polynomial in one variable as there is both x and y.
Is x
^{
2
}
+ 24y + 1 a polynomial in one variable?
-a-
Since there are two variables – x and y
It is not a polynomial in 1 variable
-ea-
Is y ^{ 4 } – 10 a polynomial in one variable?
-a-
y ^{ 4 } – 10 = y ^{ 4 } – 10y ^{ 0 }
Here power are 4 and 0.
Since all powers are whole numbers, it is a polynomial
And since there is only one variable y,
It is a polynomial in one variable
-ea-
Is 5x ^{ -2 } + 1 a polynomial in one variable?
-a-
Since power is -2
And -2 is not a whole number,
It is not a polynomial in one variable
-ea-
Is 3x ^{ 1/2 } + 2 a polynomial in one variable?
-a-
Since power is 1/2
And 1/2 is not a whole number,
It is not a polynomial in one variable
-ea-
Is 3 a polynomial in one variable?
-a-
3 = 3x ^{ 0 }
Since power is 0
And 0 is a whole number,
It is a polynomial.
And since there is only 1 variable x,
It is a polynomial in one variable
-ea-
Note:
Constant numbers are also polynomials.
Example: 2, 3, 100, -988999 are all polynomials