Question 78
Given the polynomial $P(X) = X^{4} + \square X^{3} + \square X^{2} + \square X + \square$, in which each square represents a gap where a coefficient will be placed, the next game is proposed between two players: Alternatively, the first and the second player choose an empty hole and place a non-zero integer in it until they fill all the four holes. If the resulting polynomial has at least two entire roots, the second player wins, otherwise the winner is the first. Prove that, choosing the right strategy, the first player can always win.