MATH 371 Assignment #7 (Due Wednesday, September 24)

1. A polynomial P(z) of degree 5 has roots of 3, 1+i, and 1-i, with multiplicities of 1,2,2 respectively and P(2) = 16. Find P(z).

2. Let P(z) = z³ -3z² + 2z +4. Expand P(z) as a polynomial in (z - 2) and again in (z + i) .

3. Fully factor the polynomial P(z) = z³ + (i – 2)z² + (2 – 2i)z +2i.