#(x^3 -6x^2 + 5x + 12)#
Since the sum of the coefficients of the terms is zero, #x +1# is a factor.
Using synthetic division,
#color(white)(aaa) -1 color(white)(aaa)|color(white)(aaa)1color(white)(aaa)-6color(white)(aaa)5color(white)(aaa)12#
#color(white)(aaaaaaaaa)|color(white)(aaa)darrcolor(white)(aa)-1color(white)(aaa)7color(white)(a)-12#
#color(white)(aaaaaaaaa)|………………………#
#color(white)(aaaaaaaaaaaaaa)1color(white)(aaa)-7color(white)(aaa)12color(white)(aaa)0#
#=> (x+1) (x^2 - 7x + 12)#
#=> (x+1)(x^2 - 3x - 4x + 12)#
#=> (x + 1) (x(x - 3) -4 (x-3))#
#=> (x+1)(x-3)(x-4)#
Factors are #x = -1, 3, 4#
