What must be subtracted or added to $p (x) = 8 x^{4} + 14 x^{3} - 2 x^{2} + 8 x - 12$ . so that $4 x^{2} + 3 x - 2$ is a factor of $p (x)$ ?

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Solution

Remainder is $15 x - 14$ which should be subtracted from p(x) so that $4 x^{2} + 3 x - 2$ becomes the factor of p(x)$

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p (x) = 8 x^{4} + 14 x^{3} - 2 x^{2} + 8 x - 12

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2 x^{2} - x + 1 ?

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