(iii) z3−2z2+16z−32z^3 - 2z^2 + 16z - 32z3−2z2+16z−32 Solution Group terms:(z3−2z2)+(16z−32)=z2(z−2)+16(z−2)Factor out (z−2):=(z−2)(z2+16)Now factor z2+16=z2−(4i)2:z2+16=(z−4i)(z+4i)Therefore:z3−2z2+16z−32=(z−2)(z−4i)(z+4i)\begin{aligned} & \boxed{\text{Group terms:}} \\ \\ & (z^3 - 2z^2) + (16z - 32) = z^2(z - 2) + 16(z - 2) \\ \\ & \boxed{\text{Factor out }(z - 2):} \\ \\ & = (z - 2)(z^2 + 16) \\ \\ & \boxed{\text{Now factor } z^2 + 16 = z^2 - (4i)^2:} \\ \\ & z^2 + 16 = (z - 4i)(z + 4i) \\ \\ & \boxed{\text{Therefore:}} \\ \\ & z^3 - 2z^2 + 16z - 32 = (z - 2)(z - 4i)(z + 4i) \end{aligned}Group terms:(z3−2z2)+(16z−32)=z2(z−2)+16(z−2)Factor out (z−2):=(z−2)(z2+16)Now factor z2+16=z2−(4i)2:z2+16=(z−4i)(z+4i)Therefore:z3−2z2+16z−32=(z−2)(z−4i)(z+4i)