With the help of the remainder theorem. find the remainder when the polynomial $x^{3}+7 x^{2}+17 x+25$ is divided by $x+4$
With the help of the remainder theorem. find the remainder when the polynomial $x^{3}+7 x^{2}+17 x+25$ is divided by $x+4$
Here, $p(x)=x^{3}+7 x^{2}+17 x+25$
Putting $x+4=0,$ i.e., $x=-4,$ we get
$p(-4)=(-4)^{3}+7(-4)^{2}+17(-4)+25$
$=(-64)+7(16)-68+25$
$=-64+112-68+25$
$=-132+137$
$=5$
So, by the remainder theorem, $5$ is the remainder when $x^{3}+7 x^{2}+17 x+25$ is divided by $x+4$
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