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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 x1
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) (x1) +2......(2)

Equation (2) is in the form of :

dividend=divisor×quotient+remainder

So, quotient = x1



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