factors of x^12 -1 of form x^4 + bx^3 +cx^2 + dx + e w/ rtnl coeff.

[popcorn123]

List all polynomials of the from [x^4 + bx^3 +cx^2 + dx + e ] with rational coeficients that are facts of the polynomial x^12 - 1

 

[Ishuda]

List all polynomials of the from [x^4 + bx^3 +cx^2 + dx + e ] with rational coeficients that are facts of the polynomial x^12 - 1

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

Hint: I would start by factoring x¹² - 1. This is an a²-b² expression so
x¹² - 1 = (x⁶ + 1) (x⁶ - 1) = (x⁶ + 1) (x³ + 1) (x³ - 1) = ...

 

[stapel]

List all polynomials of the from [x^4 + bx^3 +cx^2 + dx + e ] with rational coeficients that are facts of the polynomial x^12 - 1

Starting with the hints provided in a previous reply, and adding in what you've learned about the Rational Roots Test (refresh here), how far have you gotten? Where are you bogging down? Please show all of your steps and reasoning so far. Thank you!