According to the fundamental theorem of algebra, the "Maximum" number of real zeroes is equal to the highest exponent. However, there is no guarantee that all the zeroes will be "real" ... some may be imaginary.
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You can use Descartes' Rule of Signs to find the maximum number of possible real zeros. The number of sign changes in the function f(x) equals the maximum number of possible positive real zeros. The number of sign changes in the function f(-x) equals the maximum number of possible negative real zeros.Check out these examples:http://www.purplemath.com/modules/drofsign.htm