+1911 A polynomial with integer coefficients is of the form
\[21x^4 + a_3 x^3 + a_2 x^2 + a_1 x - 28 = 0.\]
If $r$ is a rational root of this polynomial, then find the number of different possible values of $r.$
+129850 Rational Roots Theorem
Possible factors of 28 = ±1, ±2 , ±4, ±7, ±14, ±28
Possible factors of 21 = ±1, ±3, ±7, ±21
Possible rational roots =
All possible factors of 28 / All possible factors of 21 =
±1, ±2, ±4, ±7, ±14, ±28, ±1/3 , ±2/3, ±4/3 , ± 4/3, ±7/3, ±14/3, ±28/3, ± 1/7, ±2/7,±4/7, ±1/21, ±2/21, ±4/21,
