If $x + 2$ is a factor of $x^{3} - 2 a x^{2} + 16$ , then find the value of a.

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Solution

The correct option is B 1
Let $p (x) = x^{3} - 2 a x^{2} + 16$
and $g (x) = x + 2$ .
If x - a is a factor of p(x), then $p (a) = 0$ .
Put $g (x) = 0$
$x + 2 = 0$
$x = - 2$
$p (- 2) = (- 2)^{3} - 2 a (- 2)^{2} + 16 = 0$
$\Rightarrow - 8 - 8 a + 16 = 0$
$\Rightarrow a = 1$

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