Let #f(x)=x^3-7x+6#

#f(1)=1-7+6=0#

Therefore,

#(x-1)# is a factor

To find the other factors, we do a long division

#color(white)(aaaa)##x^3##color(white)(aaaaa)##-7x+6##color(white)(aaaaaa)##∣##x-1#

#color(white)(aaaa)##x^3-x^2##color(white)(aaaa)####color(white)(aaaaaaaaaa)##∣##x^2+x-6#

#color(white)(aaaaa)##0+x^2-7x#

#color(white)(aaaaaaa)##+x^2-x#

#color(white)(aaaaaaaa)##+0-6x+6#

#color(white)(aaaaaaaaaaaa)##-6x+6#

#color(white)(aaaaaaaaaaaaa)##-0+0#

Therefore,

#(x^3-7x+6)/(x-1)=x^2+x-6=(x+3)(x-2)#

So,

#(x^3-7x+6)=(x-1)(x+3)(x-2)#