posted by George .
Given a polynomial and one of its factors, find the remaining factors of the polynomial. Some of the factors may not be binomials.
This is an exercise in polynomial long division. Divide 169x^3 -1690x^2 -9x +90 by x-10 to get the quotient, which is 169 x^2 - 9. That happens to be the difference of the squares of 13x and 3. So it is possible to factor the quotient one more time.
If you need to review polynomial long division, see
This division turns out to be an easy one, with no remainder.
The complete answer is
169x^3 - 1690x^2 - 9x + 90
= (x-10)(13x + 3)(13x - 3)