Question

use the rational zero's theorem to list the potential zero's of the polynomial function. Do not attempt to find the zero's f(x)=-169x^7-x^6+x+13 and then the second part is find the potential rational zero's.

Answer 1

any rational zeros have numerators which divide 13 and denominators which divide 169. That means

±(1,13)/±(1,13,169)
or,
±1 ±13 ±1/13 ±1/169

A little synthetic division shows that there are no rational roots.