x3-8x2+25x-26=0. If x=0 then the left-side=-26. Let x=1, then 1-8+25-26=-8. Let x=2, then 8-32+50-26=0, so 2 is a root. To find out the quadratic q(x) such that (x-2)q(x)=0 then we can use synthetic division:
2 | 1 -8 25 -26
1 2 -12 | 26
1 -6 13 | 0 = x2-6x+13 and q(x)=x2-6x+13. q(x)=0 has complex roots, which we can find.
x2-6x+13=0,
x2-6x=-13,
x2-6x+9=9-13=-4 (completing the square.
(x-3)2=-4,
x-3=±2i, so the other two roots are x=3+2i and 3-2i.
SOLUTION: x=2, 3+2i, or 3-2i.