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A fifth degree polynomial (could or must) have 5 linear factors. The factors (could, but do not have to be, or must) be distinct.

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JeanaShupp

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 .




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