Form a polynomial with with real coefficient having the given degree and zeros

Question

Degree: 5

Zeros: 8, - i, -9+i

Answer 1

The polynomial (x-8) is of degree 1 and has a zero at 8.

The polynomial x^2+1 has degree 2 and has two zeros at +i and -i.

The polynomial x^2+18x+82 has degree 2 and has two zeros at the numbers (-9+i) and (-9-i).

Hence, the product (x-8)(x^2+1)(x^2+18x+82) is a polynomial of degree 5 with real coefficients and zeros at all the previously mentioned points.