Find the value of a for which (x + 1) is a factor of


Find the value of $a$ for which $(x+1)$ is a factor of $\left(a x^{3}+x^{2}-2 x+4 a-9\right)$.



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

It is given that (+ 1) is a factor of f(x).

Using factor theorem,  we have


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

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

$\Rightarrow 3 a-6=0$

$\Rightarrow 3 a=6$

$\Rightarrow a=2$

Thus, the value of a is 2.


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