# what is the fastest way of factorising a cubic equation

For example i need to factorise the equation $x^3-6x^2+11x-6=0$ I know the method of putting values in the equation and then check for which value the equation becomes zero (here for x=2 the equation is zero) then I divide the equation by x-2 by long division method and I get the quotient but the process is lengthy .

isn't there any other way for saving time?

• The rational zero theorem is the way to go – imranfat Sep 6 '16 at 15:45
• I really don’t think that the method you describe is at all time-consuming. – Lubin Sep 6 '16 at 15:50
• @Lubin time consuming since I have to keep checking the output for many values – danny Sep 6 '16 at 15:54

you can depend on $(x-1)^3=x^3-3x^2+3x-1$ so $$x^3-6x^2+11x-6=x^3-3x^2-3x^2+3x+8x-1-5$$ $$(x-1)^3-3x^2+8x-5$$ $$(x-1)^3-(x-1)(3x-5)$$