The theorem of rational solutions states that, given a polynomial with integer coefficients, every potenial rational solution is written as [tex] \frac{p}{q} [/tex], where [tex] p [/tex] divides the constant term, and [tex] q [/tex] divides the leading term.
So, our choices for [tex] p [/tex] are [tex] \pm 1, \pm 3 [/tex], while our choices for [tex] q [/tex] are [tex] \pm 1, \pm 3, \pm 5, \pm 15 [/tex].
Combine all possible numerator and denominator to get all the potenial rational solutions:
[tex] \pm\frac{1}{1},\pm\frac{1}{3},\pm\frac{1}{5},\pm\frac{1}{15}[/tex]
[tex] \pm\frac{3}{1},\pm\frac{3}{3},\pm\frac{3}{5},\pm\frac{3}{15}[/tex]
