Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. (2 points) 4, -8, and 2 + 5i

Answer 1

2+5i is complex, and MUST be accompanied by its conjugate, 2-5i.

Thus, the factors of this 4th degree poly are (x-4)(x+8)(x-2-5i)(x-2+5i).

Multiply this out to obtain the poly in question.  Then arrange the powers of x in descending order, beginning with x^4.