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Division Algorithm for a Polynomial

When x2-4 x+1...

Question

When $x^{2} - 4 x + 11$ is divided by $x - 2$ , the sum of quotient and remainder is .

A

x + 2

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B

x + 5

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C

x + 4

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D

2

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Solution

The correct option is B x + 5
Dividend = Divisor × Quotient + Remainder

$x - 2) x^{2} - 4 x + 11 (x - 2_{-} x^{2} \mp 2 x - -------- - - 2 x + 11 \mp 2 x \pm 4 - -------- - 7$

Sum of quotient and remainder
$= x - 2 + 7 = x + 5$

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