Answer: A fifth degree polynomial could have 5 linear factors. But the factors do not have to be be distinct.
Explanation:
- The fundamental theorem of algebra tells that every non-constant single-variable polynomial with complex coefficients has at least one complex root.
- Corollary to the fundamental theorem tells that every polynomial of m>0 degree has exactly m zeroes.
Thus by corollary to fundamental theorem of algebra, a fifth degree polynomial must have 5 zeroes . But A fifth degree polynomial could have 5 linear factors if all zeroes are real numbers.
The factors could be distinct or similar.
Thus , The factors do not have to be distinct .