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asked Nov 15, 2021 81.5k views

1 Answer

Shadie · Answer 1 · 2021-11-22T03:15:41+0000

Answer:

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).