Answer
See answers below
Work Step by Step
Given: $f(x)=x^3+7x^2+2x+14$
Factors of the constant term: $\pm 1, \pm2,\pm7,\pm14$
Factors of the leading coefficient: $\pm 1$
Possible rational zeros: $\pm\frac{1}{1}, \pm\frac{2}{1},\pm\frac{7}{1}, \pm\frac{14}{1}$
Simplified list of possible zeros: $\pm 1, \pm2,\pm7,\pm14$
The error is all the negative numbers were forgotten.
