one of the zeros of the function f(x)=x^4+2x^3-13x^2-38x-24 is x=-3, find the other zeros of the function

Question

irishboy123 · Answer

obvious approach

long divide 

    $x^4+2x^3-13x^2-38x-24$ 

by 

     $x+3$

anonymous · Answer

@IrishBoy123  could you use synthetic division?

anonymous · Answer

idgi

irishboy123 · Answer

of course, you can do anything you like

i am starting to think that this looks like it needs the Rational Root Theorem, despite the bad clues that were left lying around

In which case, i summon the master:  @welshfella

welshfella · Answer

+/- 1 , +/- 2 +/- 4 are some of the possible roots

welshfella · Answer

f!1) =   not = 0
f(-1) = 0   so -1 is one root

welshfella · Answer

you could now divide  the function by (x + 3)( x + 1)  to get another quadratic which you can solve

welshfella · Answer

or compute  f(2) f(-2,)  f(4), f(-4)

welshfella · Answer

the first option would probably be the quickest

welshfella · Answer

use synthetic division