By Vieta's formula, we know that there must exist a factor that is x2-2x+a,
therefore we can let the factors of the initial equation be
x2-2x+a
x ) x2+bx+c
1. We know that the coefficient of x3 is 0,
therefore, b-2=0 → b=2.
2. We know that the coefficient of x2 is -10,
hence, a+c-2b=-10 → a+c=-6
3. We know that the coefficient of x is 8,
thus -2c+ab=8 → a-c=4
4. By a+c=4, a-c=4 we know a=-1, c=-5
therefore, k=ac=5
5. By those above, we could find out:
initial equation
→(x2-2x-1)(x2+2x-5)=0
Thanks, I've corrected it