The given zero has a conjugate=4i, so we have (x-4i)(x+4i)=x2+16 as a factor of P.
Algebraic long division:
x3-3x2 +3x -1 = (x-1)3
x2+16 ) x5-3x4+19x3-49x2+48x-16
x5 +16x3
-3x4 +3x3-49x2
-3x4 -48x2
3x3 -x2+48x
3x3 +48x
-x2 -16
-x2 -16
0
P(x)=(x2+16)(x-1)3, so the zeroes are -4i, 4i, 1 (three times).