If $(x - 1)$ divides $m x^{3} - 2 x^{2} + 25 x - 26$ without remainder, find the value of $m$ .

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Solution

The correct option is C
3

$p (x) = m x^{3} - 2 x^{2} + 25 x - 26$

Given, $p (1) = 0$

$\Rightarrow m (1)^{3} - 2 (1)^{2} + 25 (1) - 26 = 0$

$\Rightarrow m - 2 + 25 - 26 = 0$

$\Rightarrow m = 3$

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