if x2-1 is a factor of ax4+bx3+cx2+dx+e, show that a+c+e=b+d=0

Hello student, Please find the soluiton

if x²-1 is a factor of ax⁴+bx³+cx²+dx+e
=> x = +1 and -1 are the roots of ax⁴+bx³+cx²+dx+e

Now if f(x) = ax⁴+bx³+cx²+dx+e
than f(+1)=f(-1)=0
so a+b+c+d+e=0 ….….….(1)
and a-b+c-d+e = 0 ….…....(2)

Hence from (1) and (2),
a+c+e=b+d=0
I hope the solution is clear

Thank you