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Question

When x4+x32x2+x+1 is divided by x1, 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
By division algorithm,
f(x)=g(x)×q(x)+r(x)
where f(x) dividend
g(x) divisor
q(x) quotient
r(x) remainder

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

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



q(x)=x3+2x2+1


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