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Division Algorithm for a Polynomial

On dividing p...

Question

On dividing polynomial p (x) by 3x +1, the quotient is 2x-3 and the remainder is -2 . Find p ( x).

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Solution

$p (x) =$ (dividant x quotient) + remainder
$= (3 x + 1) . (2 x - 3) + (- 2)$
$= 6 x^{2} - 9 x + 2 x - 3 - 2$
Hence, $p (x) = 6 x^{2} - 7 x - 5$

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