Do the values of polynomials go on infinity or stop at a certain value?

A polynomial is an expression of finite length formed of
variables and constants  using only operations of addition, subtraction, multiplication
and non-negative whole number exponents. Some examples are
:

p(x) = a0+a1x+a2x^2+a^3+.....an*x^n, is a polynomial is a
sigle vwriable with n terms.

p(x) = x.  A polynomial with a
single term . (Alsocalled monomial).

p(x) = a+bx.  Also
called binomial.

The following are not
examples:

p(x) = 5/x. Reason 1/x or x^(-1) has no
non-negative whole number exponent.

p(x) =  x^2+ x^3/2. The
second term has an exponent which is not a whole
number.

Question:

"Do the
value of a polynomial go on infinity ?..." Hope  you mean whether the polynomial goes on
increasing and approaches infinity as x tends to
infinity.

To decide whether a polynomial increases or
decreases depends on the leading term (or the term with highest exponent) and its
coefficient. If the coefficient of the leading term is positve, the polynomial increses
otherwise it decreases along with x.

The polynomial 
aproaches infinity as x --> infinity if the leading term has a positive
coeffcient. It aproaches minus infinity as x-->infinity ,if the leading term has
a negative coefficient. A plynomial p(x) cannot go for a definite limit when the x (or
the variable) approaches plus or minus infinity.(Please do not get confused with
convergence of a series for |x| <1 and  limit of the nth term a, x^n for large
n). P(x) does not take a finite limit as x--> infinity (or minus infinity).
unless it is polynomial with only a constant
term.

Example : p(x) = x approaches infinity
as x-->inf.

p(x) = x^2  - x approaches ifinity as
x-->plus ifinity or x --> minus infinty, as the  term is x^2 has a
positive coefficient and x ^2