With help of remainder theorem. examine whether x+2 is a factor of polynomial x^{3}+9 x^{2}+26 x+24

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2. Polynomials

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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.

Option A

Option B

Option C

Option D

Solution

$p(x)=x^{3}+9 x^{2}+26 x+24$ 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 $x^{3}+9 x^{2}+26 x+24$

Standard 9

Mathematics

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