Let P(x)=x4+ax3+bx2+cx+dP(x) = x^4 + ax^3 + bx^2 + cx + dP(x)=x4+ax3+bx2+cx+d. If (x−1)(x-1)(x−1) and (x+1)(x+1)(x+1) are factors of P(x)P(x)P(x), which of the following must be true?
P(1)=0P(1) = 0P(1)=0 and P(−1)=0P(-1) = 0P(−1)=0
P(1)=1P(1) = 1P(1)=1 and P(−1)=1P(-1) = 1P(−1)=1
a+c=0a + c = 0a+c=0
b+d=0b + d = 0b+d=0