A polynomial with integer coefficients is of the form \[9x^4 + a_3 x^3 + a_2 x^2 + a_1 x + 15 = 0.\]Find the number of different possible rational roots of this polynomial.
Possible rational roots
All Factors of 15 / All Factors of 9
Factors of 15 = 1,3,5,15
Factors of 9 = 1,3, 9
So....
± [ 1, 1/3 , 1/9 , 3 , 5 , 5/3 , 5/9, 15 ]
