Factoring polynomials

1. Sep 30, 2012

Fabio010

z^4-4z^3+6z^2-4z-15 =0

How can i factor this polynomial in order to find the solutions??

I tried with the ruffini' rule.

and i reached the following equation [(z+1)(-z^3-5z^2+11z-15)] =0

now how can i factor (-z^3-5z^2+11z-15) ???

i tried it, but i can not solve it... :/

2. Sep 30, 2012

alberto7

Proceed with Ruffini. You'll find another root (because the problem is easy) and the remaining factor is quadratic, whose solutions you get with the formula.

3. Sep 30, 2012

Fabio010

the solutions are

-1; 3; 1+/-2i

i am going to try with ruffini again.

4. Sep 30, 2012

Fabio010

i cant. Even knowing the solutions, i can not proceed with ruffini's rule.
Maybe something is escaping me.

5. Sep 30, 2012

alberto7

Redo the quotient (z^4-4z^3+6z^2-4z-15)/(z+1), since the leading term must be z^3, not -z^3.

6. Sep 30, 2012

Fabio010

ok it now makes sense.

now i factor it

(z^3-5z^2+11z-15)/(z-3)

...

but without the solution i would never be able to discover that i should divide (z^3-5z^2+11z-15) by (z-3)

7. Sep 30, 2012

alberto7

Do Ruffini again: try with the divisors of -15 of both signs.