A polynomial with integer coefficients is of the form
9x4+a3x3+a2x2+a1x+27=0.
Find the number of different possible rational roots of this polynomial.
+605 From the rational root theorem, the denominator of the root divides 27 and the numerator divides 9. Keeping in mind that negatives are allowed, the answer is (2d(9))(2d(27)) where d(x) denotes the number of divisors of x (which is really easy to manually calculate).
