![Polynomials - Part 2](https://d1avenlh0i1xmr.cloudfront.net/ddbfe8ee-5312-46d1-ae50-4b254b0bcf59/slide3.jpg)
![Polynomials - Part 3](https://d1avenlh0i1xmr.cloudfront.net/0a9646db-4fa9-4129-84b6-2ebc07d432fa/slide4.jpg)
![Polynomials - Part 4](https://d1avenlh0i1xmr.cloudfront.net/41c9602c-61d9-4d26-95cf-40342a2f163e/slide5.jpg)
![Polynomials - Part 5](https://d1avenlh0i1xmr.cloudfront.net/ad2b6e6e-6930-4ceb-9d96-a79f2b585a26/slide6.jpg)
![Polynomials - Part 6](https://d1avenlh0i1xmr.cloudfront.net/012bf257-402e-40bb-995e-48c7967432a1/slide7.jpg)
![Polynomials - Part 7](https://d1avenlh0i1xmr.cloudfront.net/fc435265-3b0e-4e84-9f24-dbe9e7aaaea2/slide8.jpg)
![Polynomials - Part 8](https://d1avenlh0i1xmr.cloudfront.net/e4594916-2aee-49e4-856d-ea681a3a4180/slide9.jpg)
![Polynomials - Part 9](https://d1avenlh0i1xmr.cloudfront.net/e02d6e00-8960-4265-884d-0eb55e358d4f/slide10.jpg)
![Polynomials - Part 10](https://d1avenlh0i1xmr.cloudfront.net/dcb3145e-5f40-4fb9-93c6-e84e947f0a72/slide11.jpg)
![Polynomials - Part 11](https://d1avenlh0i1xmr.cloudfront.net/68822cad-7449-45c7-abcb-5e2426eb3a8c/slide12.jpg)
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