# Thread: Quick question on graphs and modular arithmetic

1. ## 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 ?

2. 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 ?

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

Tonio

3. They both cross the origin?

4. Originally Posted by zhupolongjoe
They both cross the origin?

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

Tonio

5. The same....so they have the same y-intercept?

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

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

Tonio