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Long Division of Polynomials

When a polyno...

Question

When a polynomial is divided by (x+2), the quotient and remainder are (2x-1) and 3 respectively.

6 x^{2} + 3 x + 9

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2 x^{2} + 3 x + 1

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2 x^{2} + 6 x + 11

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Solution

The correct option is B $2 x^{2} + 3 x + 1$
We know that, by divison algorithm,
Dividend = Divisor x Quotient + Remainder.

$∴ P (x) = (x + 2) \times (2 x - 1) + 3 = x (2 x - 1) + 2 (2 x - 1) + 3 = 2 x^{2} - x + 4 x - 2 + 3 P (x) = 2 x^{2} + 3 x + 1$

$∴ The required polynomial is 2 x^{2} + 3 x + 1.$

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