How about this one?
x4 – x3 + 7x2 – 9x – 18

Question

How about this one?
x4 – x3  + 7x2 – 9x – 18

anonymous · Answer

This one is actually easier

saifoo.khan · Answer

H.O.W.?

anonymous · Answer

substitute x by (u - B/(4A)), which is  u - 1/4, and then expand

saifoo.khan · Answer

o_O
No idea. LOL.

anonymous · Answer

expansion leads to $$u^4-2u^3+\frac{65u^2}{8}-\frac{51u}{4}-\frac{3915}{256}$$

saifoo.khan · Answer

lol, still no idea.

anonymous · Answer

$$x^4-x^3+7 x^2-9 x-18=(x-2) (x+1) \left(x^2+9\right)  $$

saifoo.khan · Answer

H.O.W.?

anonymous · Answer

I did a mistake somewhere, since u^3 remains :-P

anonymous · Answer

I guess the method is complex :-P

try doing the posible rational roots and trial & error method

anonymous · Answer

possible rational roots +-(1, 2, 3, 6, 9, 18)

turingtest · Answer

I would try to plug in low numbers and look for a zero. I would hopefully have tried 2 OR -1 which would have given me a zero and then divide the polynomial out

anonymous · Answer

why do you have these questions? your teacher wants you to burn :-D ?

saifoo.khan · Answer

Trial and error sounds the best. 
haha @adg

anonymous · Answer

im full now :p

anonymous · Answer

and the food tasted great! goodluck with ur problems seafood...

saifoo.khan · Answer

lol, thanks.

saifoo.khan · Answer

but when x = 1, im getting 20

saifoo.khan · Answer

-20

anonymous · Answer

From prior experience it appears that Mathematica can factor any expression that is factorable.  I have no idea what factoring algorithms have been incorporated.

saifoo.khan · Answer

but when x = 1, im getting -20

turingtest · Answer

you tried x=-1 ? that's the root supposedly

saifoo.khan · Answer

damn!!

saifoo.khan · Answer

my bad. LOL

saifoo.khan · Answer

Thanks guys.

turingtest · Answer

you know how to divide polynomials right?

saifoo.khan · Answer

Yes i do know.

saifoo.khan · Answer

Both synthetic and another one.

saifoo.khan · Answer

Long division.

turingtest · Answer

then that's all I got

saifoo.khan · Answer

Wait, how can i solve this by that way? :D

turingtest · Answer

When you divide the polynomial by (x-1) you should get another cubic. Then you have to find that 2 is also a root. 
You could use Descartes' Rule of signs to tell you how many negative or positive roots a polynomial has, so using that could save you some time there.
Once you divide out the (x-2) you have a nice quadratic we all love so much.