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Question

# When x4+x3âˆ’2x2+x+1 is divided by x-1, the remainder is 2 and the quotient is q(x). Find q(x).

A
x3+2x2+x+1
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B
x3+x2+x
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C
x3+2x2+1
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D
x3+x2+1
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Solution

## The correct option is C x3+2x2+1Given: Dividend = x4+x3−2x2+x+1Divisor = x−1Remainder = 2 We know that, by division algorithm, dividend = divisor ×quotient + remainder. ⇒x4+x3−2x2+x+1=(x–1)q(x)+2 x4+x3−2x2+x−1=(x−1)q(x) q(x)=x4+x3−2x2+x−1(x–1) x3+2x2+1x−1x4+x3−2x2+x−1x4−x3 ––––––––––––––––2 2x3−2x2+x−1 2x3−2x2 ––––––––––––––––––––––– x−1 x−1––––––––––––––– 0 So, q(x)=x3+2x2+1.

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