If $x - 1$ is a factor of the polynomial $3 x^{2} + m x$ then the value of $m$ is ......

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Solution

$(x - 1)$ is a factor of $3 x^{2} + m x$

Then upon dividing it. The remainder should be equal to zero.

$x - 1) 3 x^{2} + m x (3 x$
$3 x^{2} + 3 x$
_______________
$m x + 3 x$

$∴ m x + 3 x = 0$

$\Rightarrow (m + 3) x = 0$

$\Rightarrow m + 3 = 0$ or $x = 0$

$\Rightarrow m = - 3$

Hence, the value of $m$ is $- 3$ .

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