Question
The greatest whole number, by which the expression n4 + 6n3 + 11n2 + 6n + 24 is divisible for every natural number n , is -
Answer: Option D $$\eqalign{
& {\text{According to the question,}} \cr
& {{\text{n}}^4} + 6{{\text{n}}^3} + 11{{\text{n}}^2} + 6{\text{n + 24}} \cr
& {\text{put n = 1}} \cr
& = 1 + 6 + 11 + 6 + 24 \cr
& = 48 \cr
& {\text{put n = 2}} \cr
& {\text{ = 16 + 48 + 44 + 12 + 24}} \cr
& {\text{ = 144}} \cr
& {\text{Clearly it is divisible by 48}} \cr} $$
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