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This guy is a fifth degree polynomial:

f ( x ) = x^5 - 7x + 3

*The highest power on these wins!

Here's a fourth degree polynomial:

f ( x ) = 9x^2 - 3x^4

So, what's the degree on this guy?

f ( x ) = 5x - 7


It's really 
  f ( x ) = 5x^1 - 7

So, it's a first degree polynomial.

Here's a tricky one:

f ( x ) = 3

Hmm...  there's NO x guy at all...  that's ZERO x guys...  So, it's a zero degree polynomial!

You can also write it like

f ( x ) = 3x^0


TRY IT:

What are the degrees of these polynomials?

f ( x ) = 7x^6 - 8x^4 - 2

f ( x ) = 5 - x^2 - x^3