Answer: See below
Step-by-step explanation:
[tex]$Find the possible rational roots using the rational root theorem:$x^{3}+x^{2}-3 x+12=0$Select the coefficient of the leading term and the constant term:$1 x^{3}+x^{2}-3 x+12=0$\\Find the positive divisors of 12 and 1: \\\\Divisors of $12: 1,2,3,4,6,12$\\Divisors of $1: 1$\\Divide each of the divisors of 12 by 1 :\\$\frac{1}{1}, \frac{2}{1}, \frac{3}{1}, \frac{4}{1}, \frac{6}{1}, \frac{12}{1}$2, \pm 3, \pm 4, \pm 6, \pm 12$[/tex]
[tex]$Because both positive and negative values are valid candidates, the possible rational roots of $x^{3}+x^{2}-3 x+12=0$ are:$\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12[/tex]
