A Laurent
polynomial in
x (over a
field k)
is an expression of the form
a-nx-n+...+a0+a1x+...+amxm
where the
coefficients
ai lie in
k. (You can take
k to be the
real numbers or
complex numbers.)
For example, 10+5x, x-1, and x-2+3x2
are all Laurent polynomials.
They can be added and multiplied in just the way you expect (so that x.x-1=1)
and the collection k[x,x-1] of all Laurent polynomials
forms a commutative ring.