Answer:
[tex]x+2[/tex]
Step-by-step explanation:
If [tex]P(x)[/tex] is a polynomial and [tex]x+a[/tex] is a factor of polynomial the [tex]p(-a)=0[/tex]
check [tex]x+3[/tex] that is [tex]x=-3[/tex]
[tex]P(-3)=-(3)^3-5(-3)^2-2(-3)+24\\=-27-5\times9+6+24\\=-27-45+6+24\\=-72+30\\=-42[/tex]
Hence [tex](x+3)[/tex] is not a factor of [tex]P(x)[/tex].
[tex]Check\ (x+1)\ that\ is\ x=-1\\P(-1)=(-1)^3-5(-1)^2-2(-1)+24\\=-1-5+2+24\\=-6+26\\=20[/tex]
Hence [tex](x+1)[/tex] is not a factor of [tex]P(x)[/tex].
Check [tex](x+2)[/tex] that is [tex]x=-2[/tex]
[tex]P(-2)=(-2)^3-5(-2)^2-2(-2)+24\\=-8-20+4+24\\=-28+28\\=0[/tex]
Hence [tex](x+2)[/tex] is a factor of [tex]P(x).[/tex]
