Question

Help with this question, please!

Answer 1

Answer:

$x+2$

Step-by-step explanation:

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

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

$P(-3)=-(3)^3-5(-3)^2-2(-3)+24\\=-27-5\times9+6+24\\=-27-45+6+24\\=-72+30\\=-42$

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 $P(x).$