With help of remainder theorem. remainder when polynomial x^{3}+7 x^{2}+17 x+25 is divided by x+4

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2. Polynomials

medium

With the help of the remainder theorem. find the remainder when the polynomial $x^{3}+7 x^{2}+17 x+25$ is divided by $x+4$

Option A

Option B

Option C

Option D

Solution

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 $x+4$

Standard 9

Mathematics

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