The polynomial P(z) = z^(3) +mz^(2) +nz - 8 is divisible by (z+1+i), where z ∈C, m,n ∈R. Find the value of m and of n.

Question

The polynomial P(z) =
`z^(3) +mz^(2) +nz - 8` is divisible by (z+1+i), where z ∈C, m,n ∈R. Find the value of m and of n.

Answer 1

m=-2 n=-6

Explanation:

(z+1+i)(z+1-i)=z²+2z+1-(i²)=z²+2z+2

z³+mz²+nz-8=(z²+2z+2)(z-4)=z³-2z²-6z-8

m=-2

n=-6

If it's wrong, please delete it