Answer:
36
Step-by-step explanation:
Hello,
If [tex]X=x^2[/tex] it becomes
[tex]X^3-289X^2-X+289=(X^2-1)(X-289)[/tex]
and [tex]289=17^2[/tex]
[tex]X^2-1=(X-1)(X+1)=(x^2-1)(x^2+1)=(x+1)(x-1)(x^2+1) \\\\x^2-289=x^2-17^2=(x-17)(x+17)[/tex]
So,
[tex]x^6-289x^4-x^2+289=(x^2-1)(x^2+1)(x^2-289)=(x-1)(x+1)(x+17)(x-17)(x^2+1)[/tex]
a = 1
b = 1
c = 17
d = 17
e = 0
Then a + b + c + d + e = 36
Thanks
