Question

Choose the words or phrases that best complete the sentences.

Answer 1

Answer: A fifth degree polynomial could have 5 linear factors. But the factors   do not have to be be distinct.

Step-by-step 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 .

Answer 2

1) Could
2) Could, but don't have to be