Check whether the polynomial
$p(x)=x^{3}+9 x^{2}+26 x+24$ is a multiple of $x+2$ or not.
Check whether the polynomial
$p(x)=x^{3}+9 x^{2}+26 x+24$ is a multiple of $x+2$ or not.
$p(x)$ will be a multiple of $x+2,$ only if $x+2$ divides $p(x)$ leaving remainder zero.
Now, taking $x+2=0,$ we have $x=-2$
Also, $p(-2)=(-2)^{3}+9(-2)^{2}+26(-2)+24$
$=(-8)+9(4)-52+24$
$=-8+36-52+24$
$=-60+60$
$=0$
So, the remainder obtained on dividing $p(x)$ by $x+2$ is $0 .$
So, $(x+2)$ is a factor of the given polynomial $p(x),$ that is $p(x)$ is a multiple of $x+2$
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