If x2-1 is a factor of ax4+bx3+cx2+dx+e, then
Let f (x) = ax⁴ + bx3 + cx2 + dx + e
Since, x2- 1 is a factor of f(x)
Therefore,
f (-1) = 0
a (-1) + b (-1)3 + c (-1)2 + d (-1) + e = 0
a + c + e = b + d