P(x) is a polynomial with integral coefficients such that for four distinct integers a,b,c,d,P(a)=P(b)=P(c)=P(d)=3. If P(e)=5 (e is an integer), then

P(a)=P(b)=P(c)=P(d)=3⇒ P(x)=3 has a, b, c, d as its roots⇒ P(x)−3=(x−a)(x−b)(x−c)(x−d)Q(x)[Q(x) has integral coefficient]Given P(e) = 5, then(e−a)(e−b)(e−c)(e−d)Q(e)=5This is possible only when at least three of the five integers(e−a),(e−b),(e−c),(e−d),Q(e) are equal to 1 or -1. Hence,two of them will be equal, which is not possible. Since a, b, c,d are distinct integers , P(e) = 5 is not possible.