When a polynomial is divided by $(x + 5)$ , the quotient and the remainder are $(x^{2} + 1)$ and 3, respectively. Find the polynomial.

x^{3} + 5 x^{2} + x + 8

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x^{3} - 3 x^{2} - x + 8

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x^{3} + 5 x^{2} + x + 5

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x^{3} - 3 x^{2} + x + 5

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Solution

The correct option is A $x^{3} + 5 x^{2} + x + 8$
By using a division algorithm, we get,

p(x) = g(x) × q(x) + r(x)

By putting the values of g(x), q(x) and r(x), we get

p(x) = x³ + 5x² + x + 8

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