passing through the origin means that 0 is a root
for a polynomial with real coefients (an integer is real), if a+bi is a root, a-bi is also a root
so zeroes are
i,-i 8-i, 8+i and 0
the factors of an equation with factors r1,r2,r3 is
(x-r1)(x-r2)(x-r3)
so
zeroes of i,-i,8-i, 8+i, 0 is
(x-i)(x+i)(x-(8-i))(x-(8+i))(x-0)
expanded
[tex]x^5-16x^4+66x^3-16x^2+65x[/tex]
the polynomial is [tex]x^5-16x^4+66x^3-16x^2+65x[/tex]
