The fundamental theorem of algebra for the complex numbers states that a polynomial of degree n has n roots, counting multiplicity. This paper explores the "perplex number system" (also called the "hyperbolic number system" and the "spacetime number system") In this system (which has extra roots of +1 besides the usual [plus or minus]1 of the reals) every degree-n polynomial has exactly n[superscript 2] roots. In the case of multiple roots, we find a satisfying method of assigning multiplicity.