Question

Help with this question, please!

Answer 1

`x+2`

Explanation:

If
`P(x)` is a polynomial and
`x+a` is a factor of polynomial the
`p(-a)=0`

check
`x+3` that is
`x=-3`

`P(-3)=-(3)^3-5(-3)^2-2(-3)+24\\=-27-5*9+6+24\\=-27-45+6+24\\=-72+30\\=-42`

Hence
`(x+3)` is not a factor of
`P(x)`.

`Check\ (x+1)\ that\ is\ x=-1\\P(-1)=(-1)^3-5(-1)^2-2(-1)+24\\=-1-5+2+24\\=-6+26\\=20`

Hence
`(x+1)` is not a factor of
`P(x)`.

Check
`(x+2)` that is
`x=-2`

`P(-2)=(-2)^3-5(-2)^2-2(-2)+24\\=-8-20+4+24\\=-28+28\\=0`

Hence
`(x+2)` is a factor of
`P(x).`