$x^3 - 6x^2 + 11x - 6 = 0$
I can not reasonably factor this intuitively in any short amount of time with my skill level. Is this the only hope to solving such equations by hand? What tools can I use to help ease the pain or make it more clear to myself?
I try to:
$(x + ?)(x^2 - 6x)$ but it does not seem promising, in my eyes
I cant do anything, that I know about, with:
$x(x^2 - 6x + 11) = 6$
I don't want to give up, but I do anyway and ask my calculator, there is three solutions, alas I have no idea how that helps me (with my knowledge, it does not)!
Should I just practice with smaller polynomials more, and this one might look easier?
Any suggestions are appreciated, I will tag this as homework because it should be.