Find all the zeros of the function...

Question

haleyelizabeth2017 · Answer

$\large y=x^3-x^2-3x-9$

haleyelizabeth2017 · Answer

I'm just not sure where to start.......

jdoe0001 · Answer

hmm
how are you supposed to find them anyway?

haleyelizabeth2017 · Answer

Just one second..... :)

haleyelizabeth2017 · Answer

can't we use synthetic division?

noelgreco · Answer

Try synthetic division or the remainder theorem to get it down to a quadratic

haleyelizabeth2017 · Answer

okay :)

jdoe0001 · Answer

well... we'd need something to divide it by first

haleyelizabeth2017 · Answer

the only number they have in common is 1....so we can try that out first :)

jdoe0001 · Answer

I mean.. there are several ways to get them
but since this exercise was given, surely is covering some material already gone through

noelgreco · Answer

The rational roots theorem narrows down the possibilities in factoring out a first order binomial.

haleyelizabeth2017 · Answer

okay.......I don't remember doing the rational roots in this section.........

jdoe0001 · Answer

yes... but all alonng we're assuming she konws them or not

noelgreco · Answer

The theorem says that any roots are going to be factors of the constant (last) term over the leading coefficient.  So 
$$\frac{ \pm9 }{ 1 }\frac{ \pm3 }{ 1 }\frac{ \pm1 }{ 1 }$$
Try those w/ synthetic division - one of them gives a 0 remainder

haleyelizabeth2017 · Answer

okay so try 9, -9, 3, -3, 1 and -1? I know how to use synthetic division method, just not that theorem :)

noelgreco · Answer

yep

haleyelizabeth2017 · Answer

okay so 1 doesn't work, correct? I tried and it came out to $x^3-3x-12$........

noelgreco · Answer

1 does not work

haleyelizabeth2017 · Answer

okay.... :) let me try -1 and also 3 :)

haleyelizabeth2017 · Answer

3 works! :D
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so doesn't that leave me with $x^2+2x+3$ correct?