# Polynomial Functions

• Oct 20th 2011, 09:23 AM
richtea9
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?
• Oct 20th 2011, 09:32 AM
Youkla
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.
• Oct 20th 2011, 10:13 AM
richtea9
Re: Polynomial Functions
Quote:

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\$
• Oct 20th 2011, 10:21 AM
Youkla
Re: Polynomial Functions
Quote:

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.