Fundamental Theorem of Algebra

The statement that every nonconstant polynomial with complex coefficients has at least one complex root; equivalently, every degree-n polynomial over the complex numbers factors as a product of n linear factors when multiplicity is counted.

The statement that every nonconstant single-variable polynomial with complex coefficients has at least one complex root; equivalently, a degree-n polynomial over the complex numbers factors into n linear factors when multiplicities are counted.