$If the quotient on dividing x^{4} + 10 x^{3} + 35 x^{2} + 50 x + 29 by (x + 4) is x^{3} - a x^{2} + b x + 6, then find the value of a, b and also remainder.$

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Solution

$Let p (x) x^{4} + 10 x^{3} + 35 x^{2} + 50 x + 29$
$Standard form = x^{4} + 10 x^{3} + 35 x^{2} + 50 x + 29$

Coefficient are 1, 10, 35, 50, 29

Therefore, a =−6 , b = 11 and remainder= 5 .

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