Now, for two really important things!

So important, in fact, that we call them "theorems."

An n degree polynomial can cross or
touch the x-axis up to
n times.

Let's rephrase this guy more mathematically:

An n degree polynomial has,
at most,
n real zeros.

Here's the second one:

Remember, that on the odd degree polynomials, the tails always shoot off in opposite directions...  Right?  So...

Odd degree polynomials must cross
the x-axis, at least, once.

More mathematically:

An odd degree polynomial
has, at least, one real zero.

Get these in your head!

No room?

Who starred in The Terminator?

OK, forget that -- now you have room!