Argue whether or not g(x) could be factored completely by using only the factor theorem. Give examples to support your argument(s).

Question

You are asked to factor a quintic polynomial g(x). Argue whether or not g(x) could be factored completely by using only the factor theorem. Give examples to support your argument(s). Make sure to discuss all possibilities (real solutions, no real solutions, rational solutions, etc.).

*NOTE*

Grade 12 Advanced Functions

Please explain clearly. Thanks

Answer 1

Not possible because A5 is the unique simple non-abelian group of smallest order.