# Quick question on graphs and modular arithmetic

• Mar 25th 2010, 02:35 PM
zhupolongjoe
Quick question on graphs and modular arithmetic
Let f(x),g(x) belong to R[x] with f(x)=g(x)(mod x)...what can you say about the graphs of y=f(x) and y=g(x)? Well, this says x divides f(x)-g(x)..so one is an odd power and one an even...is there something more to say ?
• Mar 25th 2010, 03:47 PM
tonio
Quote:

Originally Posted by zhupolongjoe
Let f(x),g(x) belong to R[x] with f(x)=g(x)(mod x)...what can you say about the graphs of y=f(x) and y=g(x)? Well, this says x divides f(x)-g(x)..so one is an odd power and one an even...is there something more to say ?

$x$ divides a polynomial $p(x)$ iff the free coefficient of $p(x)$ is zero, so...

Tonio
• Mar 25th 2010, 04:07 PM
zhupolongjoe
They both cross the origin?
• Mar 25th 2010, 04:09 PM
tonio
Quote:

Originally Posted by zhupolongjoe
They both cross the origin?

No! Their difference has free coefficient = 0 so the free coefficient of each is...(!?)

Tonio
• Mar 25th 2010, 04:46 PM
zhupolongjoe
The same....so they have the same y-intercept?
• Mar 25th 2010, 06:36 PM
tonio
Quote:

Originally Posted by zhupolongjoe
The same....so they have the same y-intercept?

That's it: I think you've nailed it.

Tonio