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Question

When x4+x32x2+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+1
Given: Dividend = x4+x32x2+x+1Divisor = x1Remainder = 2

We know that, by division algorithm,
dividend = divisor ×quotient + remainder.

x4+x32x2+x+1=(x1)q(x)+2

x4+x32x2+x1=(x1)q(x)

q(x)=x4+x32x2+x1(x1)

x3+2x2+1x1x4+x32x2+x1x4x3 ––––––––––––––2 2x32x2+x1 2x32x2 ––––––––––––––––––––– x1 x1––––––––––––– 0
So, q(x)=x3+2x2+1.


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