With the help of the remainder theorem. examine whether $x+2$ is a factor of the polynomial $x^{3}+9 x^{2}+26 x+24$ or not.
With the help of the remainder theorem. examine whether $x+2$ is a factor of the polynomial $x^{3}+9 x^{2}+26 x+24$ or not.
$p(x)=x^{3}+9 x^{2}+26 x+24$ is the given polynomial and $(-2)$ is the zero of the linear polynomial $x+2$
Now, $p(-2)=(-2)^{3}+9(-2)^{2}+26(-2)+24$
$=(-8)+9(4)-52+24$
$=-8+36-52+24$
$=-60+60=0$
Hence, by the factor theorem, $(x+2)$ is a factor of $x^{3}+9 x^{2}+26 x+24$
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