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.

##
**
Polynomial
**
**
in
**
**
one
**
**
variable
**

In polynomial x
^{
3
}
− 3x
^{
2
}
+ 4x + 10

There is only variable x.

So, it is a polynomial in one variable

Is x
^{
2
}
+ 24y + 1 a polynomial in one variable?
**
**

Since there are two variables – x and y

It is not a polynomial in 1 variable

Is y
^{
4
}
– 10 a polynomial in one variable?

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

Is 5x
^{
-2
}
+ 1 a polynomial in one variable?

Since power is -2

And -2 is not a whole number,

It is not a polynomial in one variable

Is 3x
^{
1/2
}
+ 2 a polynomial in one variable?

Since power is 1/2

And 1/2 is not a whole number,

It is not a polynomial in one variable

Is 3 a polynomial in one variable?

View Answer
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

Note:Constant numbers are also polynomials.

Example: 2, 3, 100, -988999 are all polynomials