Divide the first polynomial by the second polynomial and find the remainder using factor theorem $(2 x^{3} - 2 x + a x - 2), (x - a)$

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Solution

Consider the given expression, $2 x^{3} - 2 x + a x - 2$ and $a - x$

Now,

By reminder theorem $D = Q \times d + R$

$2 x^{3} - 2 x + a x - 2 = (2 x^{2} + 2 a x + 2 a^{2} + a - 2) (x - a) + a (2 a^{2} + a - 2) - 2$

Hence reminder is , $R = a (2 a^{2} + a - 2) - 2$

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