Question

Which values are possible rational roots of 12x^3 + 14x^2 - x + 18 = 0 according to the rational root theorem?

Answer 1

Rational root theorem:

12x³, q could be ±1, ±2, ±3, ±4, ±6, ±12

18, p could be ±1, ±2, ±3, ±6, ±9, ±18

So, possible answers are:

±1/1, ±1/2, ±1/3, ±1/6, ±1/9, ±1/18, ±2/1, ±2/2, ±2/3, ±2/6, ±2/9, ±2/18, ±3/1, ±3/2, ±3/3, ±3/6, ±3/9, ±3/18, ±4/1, ±4/2, ±4/3, ±4/6, ±4/9, ±4/18, ±6/1, ±6/2, ±6/3, ±6/6, ±6/9, ±6/18, ±12/1, ±12/2, ±12/3, ±12/6, ±12/9, ±12/18

Simplifying all and taking the equals we have

±1, ±1/2, ±1/3, ±1/6, ±1/9, ±1/18, ±2, ±2/3, ±2/9, ±3, ±3/2, ±4, ±4/3, ±4/9, ±6, ±12