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Question

The value of b so that x4−3x3+5x2−33x+b is divisible by x2−5x+6, is:

A
45
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B
48
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C
51
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D
54
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Solution

The correct option is D 54
Since the given polynomial is exactly divisible by x25x+6=(x2)(x3) , it should be exactly divisible by x2 and x3 as well.
By remainder theorem, at x=2;1624+2066+b=0b=54

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