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Question

f(x)=x4+3x26x2 then the coefficient of x3 in f(x+1) is

A
24
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B
-24
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C
4
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D
-4
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Solution

The correct option is C 4
Given: f(x)=x4+3x26x2
To find the coefficient of x3 in f(x+1)
Sol: f(x)=x4+3x26x2f(x+1)=(x+1)4+3(x+1)26(x+1)2f(x+1)=x4+4x3+6x2+4x+1+3(x2+x+1)6x62
As (a+b)4=a4+4a3b+6a2b2+4ab3+b4
Hence the coefficient of x3 in f(x+1) is 4

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