Find all zeros of this function.
4i, -4i, 2
2, -2, -4i
4i+1, 4i-1, 1
4i-1, -2, 2
Write the polynomial as a product of linear factors
The possible rational zeros (according to Rational Zero test) are ±1, ±2, ±4, ±8, ±16, ±32.
To help determine which of those choices is actually a zero, take a look at the graph of h(x).
It looks like there is a rational zero at x=2, so test the factor (x-2) with synthetic division.
H(x)= x3-2x2+16x-32=(x-2)(x2+16)=(x-2)(x-4i)(x+4i) [written as a product of linear factors]
Therefore all the zeros of this function are x=2, 4i, and -4i.