1. ## Polynomial Functions

Hi people, hoping you can help me understand polynomial functions.

I have been given an example which is the following:

p(x) = 2x^3 + 3x + 1

Coefficient of x^3: 2 - I understand why this is a 2 because it is in front of x^3.
Coefficient of x^2: 0 - I understand this as there is no x to the power of 2.
Coefficient of x^1: 3 - I see why as 3 is in front of the single x.
Coefficient of x^0: 1 - However, I do not see why this is?

2. ## Re: Polynomial Functions

Because $\displaystyle x^0 = 1$. So what you really have is

$\displaystyle p(x) = 2x^3 + 3x +1x^0$ which is just $\displaystyle p(x) = 2x^3 + 3x +1$

There is no need to actually state $\displaystyle x^0 = 1$ in the polynomial since it just equals 1.

3. ## Re: Polynomial Functions

Originally Posted by Youkla
Because $\displaystyle x^0 = 1$. So what you really have is

$\displaystyle p(x) = 2x^3 + 3x +1x^0$ which is just $\displaystyle p(x) = 2x^3 + 3x +1$

There is no need to actually state $\displaystyle x^0 = 1$ in the polynomial since it just equals 1.
So the 1 and the end of the expression is representing $\displaystyle x^0$

4. ## Re: Polynomial Functions

Originally Posted by richtea9
So the 1 and the end of the expression is representing a single X?
The 1 at the end of the polynomial is just a constant. It's technically the coefficient of $\displaystyle x^0$, but like I said, we don't write $\displaystyle x^0$ in the actual polynomial itself since it just equals 1.