If $(x - 1)$ is a factor of $4 x^{3} + 3 x^{2} - 4 x + k$ , find the value of k.

-3

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Solution

The correct option is A -3
Let $p (x) = 4 x^{3} + 3 x^{2} - 4 x + k$
$g (x) = x - 1 = 0$
$x - 1 = 0$
$x = 1$
If $(x - a)$ is a factor of p(x), then $p (a) = 0$ .
$p (1) = 4 (1)^{3} + 3 (1)^{2} - 4 (1) + k = 0$
$3 + k = 0$
$k = - 3$

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