How do you factor #x^3-8x^2+17x-10#?
Polynomials of degree
One trick is to hope for an integer solution.
If an integer solution exists the constant term in the factors must be one of the factors of the constant term of the expression.
In this case the factors of
Using synthetic division to divide
(sorry I can't see any way to neatly demonstrate synthetic division here)
with obvious factors
Late addition: Here is an image to help explain the synthetic division