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Division Algorithm for a Polynomial

When a polyno...

Question

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

$2 x^{2} + 6 x + 11$

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

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$6 x^{2} + 3 x + 9$

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$2 x^{2} + 3 x + 1$

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Solution

The correct option is D
$2 x^{2} + 3 x + 1$

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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Similar questions

Quotient and remainder of a polynomial when divided by $x + 2$ are $2 x - 1$ and $3$ respectively. Find the polynomial.

p (x)

x^{2} + 3 x + 5

2 x^{2} + x + 1

x = 3

P (x)

(7 x^{2} + x + 5)

(3 x^{3} - 2 x^{2} + 7 x - 5) \div (x + 3)

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

g (x)

(3 x - 5)

(9 x + 10)

g (x)

1

2

x - 2

x - 1

x^{2} - 3 x + 2,

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