Answer
See answers below
Work Step by Step
Given: $f(x)=x^3+7x^2+2x+14$
Factors of the leading coefficient: $\pm 1, \pm2,\pm3,\pm 6$
Factors of the constant term:$\pm 1, \pm 5$
Possible rational zeros: $\pm\frac{1}{1}, \pm\frac{5}{1}, \pm\frac{1}{2}, \pm\frac{5}{2},\pm\frac{1}{3}, \pm\frac{5}{3},\pm\frac{1}{6}, \pm\frac{5}{6}$
Simplified list of possible zeros: $\pm 1, \pm5,\pm\frac{1}{2}, \pm\frac{5}{2},\pm\frac{1}{3}, \pm\frac{5}{3},\pm\frac{1}{6}, \pm\frac{5}{6}$
The error is: Numerator and denominator candidates were reversed.
