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

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Solution

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

$(x - 1)$ is a factor.

$∴ 1$ is a zero of $p (x)$

$\Rightarrow p (1) = 0$

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

$\Rightarrow 2 - 9 + 1 + k = 0$

$\Rightarrow k = 6.$

Hence, the answer is $6.$

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