Answer:
The roots are 2, 5 and 6.
Explanation:
As the last term is 60 we could see if one root is 2:
2^3 - 13(2)^2 + 52*2 - 60
= 8 - 52 + 104 - 60
= 112 - 112 = 0
So x = 2 is one root and x - 2 is a factor.
Long multiplication:
x - 2 (x^3 - 13x^2 + 52x - 60 ( x^2 - 11x + 30 <--- Quotient
x^3 - 2x^2
- 11 x^2 + 52x
- 11x^2 + 22x
30x - 60
30x - 60
So x^2 - 11x + 30 = 0
(x - 6)(x - 5) = 0
x = 6, 5.