If x +1 is a factor of ax3 +x2 -2x+4a-9,


If x +1 is a factor of ax3 +x2 -2x+4a-9, then find the value of a.


Let $p(x)=a x^{3}+x^{2}-2 x+4 a-9$

Since, $x+1$ is a factor of $p(x)$, then put $p(-1)=0$

$\therefore \quad a(-1)^{3}+(-1)^{2}-2(-1)+4 a-9=0$

$\Rightarrow \quad-a+1+2+4 a-9=0$

$\Rightarrow \quad 3 a-6=0 \Rightarrow 3 a=6$

$\Rightarrow \quad a=\frac{6}{3}=2$

Hence, the value of $a$ is $2 .$

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