Factoring polynomials

  • Thread starter Fabio010
  • Start date
  • #1
83
0
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... :/
 

Answers and Replies

  • #2
10
0
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
83
0
the solutions are

-1; 3; 1+/-2i

i am going to try with ruffini again.
 
  • #4
83
0
i cant. Even knowing the solutions, i can not proceed with ruffini's rule.
Maybe something is escaping me.
 
  • #5
10
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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
83
0
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
10
0
Do Ruffini again: try with the divisors of -15 of both signs.
 

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