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Question

# Find the quotient when divided x2+1 by x+1 using linear division method .

A
x+1
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B
2x1
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C
x1
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D
x2
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Solution

## The correct option is C x−1 x2+1 by x+1 To get the term x2 multiply x+1 by x and subtract x x (x+1) - x = x2 So, dividend = x2+1 =x (x+1) - x + 1 ......(1) To get the term - x multiply x+1 by -1 and add 1. -1 (x+1)+1 = - x So, x2+1 =x (x+1) -1 (x+1)+1 + 1 ......from (1) Hence, x2+1 = (x+1) (x−1) +2......(2) Equation (2) is in the form of : dividend=divisor×quotient+remainder So, quotient = x−1

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