1
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Question

# When a polynomial P(x) is divided by x,(x−2) and (x−3), remainders are 1, 3 and 2 respectively. the same polynomial is divided by x(x−2)(x−3), the remainder is ax2+bx+c, then the value of c is

A
3
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B
2
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C
6
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D
1
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Solution

## The correct option is B 1According to factor theoremp(x)=xq(x)+1P(x)=(x−2)q′(x)+3P(x)=(x−3)q′′(x)+2So, At x=0,P(0)=1At x=2,P(2)=3At x=3,P(3)=2Now when the polynomial P(x) is divided by (x−2)(x−3)x the remainder must have the degree less than 3 . that is the remainder will be of the form ax2+bx+c⟹P(x)=x(x−2)(x−3)q′′′′(x)+ax2+bx+cSo, P(0)=1=a(0)2+b(0)+c⟹c=1

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