##  [Fundamental Theorem of Algebra](/fundamental-theorem-algebra) 

  ##  [Fundamental Theorem of Algebra](https://mathlogic.quantumdictionary.io/fundamental-theorem-algebra-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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.

 

 

 

 

 





 

 



 ##  [Fundamental Theorem of Algebra](https://algebra.quantumdictionary.io/fundamental-theorem-algebra-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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.