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


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




$f(x)=2 x^{3}+9 x^{2}+x+k$

$(x-1)$ is a factor of $f(x)=2 x^{3}+9 x^{2}+x+k$.

$\Rightarrow f(1)=0$

$\Rightarrow 2 \times 1^{3}+9 \times 1^{2}+1+k=0$

$\Rightarrow 12+k=0$

$\Rightarrow k=-12$

Hence, the required value of is -12.


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