What must be added to $6 x^{4} - x^{3} + 3 x^{2} + 4 x - 2$ , so that the result is exactly divisible by $(3 x^{2} - 2 x + 4)$ ? Also obtain the expression that is exactly divisible.

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Solution

$R = - 2 x + 2$
$\Rightarrow$ adding $(2 x - 2)$ in given polynomial will made $R = 0$
Hence exactly divisible by $(3 x^{2} - 2 x + y)$ .

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