F(x) is a fourth order polynomial with integer coefficients and with no common factor. The roots of F(x) are –2, –1, 1, 2. If p is a prime number greater than 97, then the largest integer that divides F(p) for all values of p is

• Given that F(x)=(x+2)(x+1)(x−1)(x−2)
  Putting x=P, we have F(P)=(P+2)(P+1)(P−1)(P−2)
  Since P is a prime number, P is in form 6K±1, where K is the positive integer
  
  F(6K+1)=(6K+3)(6K+2)(6K)(6K−1)
  =(36)(2K+1)(3K+1)(K)(6K−1)——– (1)
  
  F(6K−1)=(6K+1)(6K+2)(6K)(6K−3)
  =36(6K+1)(3K+1)(K)(3K−1)——– (2)
  
  Please note that the value of K≥17 and expression F(6K+1) and F(6K–1) always bear the factor 10.
  
  Hence 360 is the correct choice.
  
  Therefore option (D) is the correct choice
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