Which of the following is the complete list of roots for the polynomial function f (x) = (x squared + 2 x minus 15) (x squared + 8 x + 17) ?

x = - 5, 3, - 4 - i, - 4 + i.

Step-by-step explanation:

(x^2 + 2x - 15) (x^2 + 8x + 17) = 0

(x^2 + 2x - 15) = 0

(x + 5) (x - 3) = 0

x = - 5, 3.

x^2 + 8x + 17 = 0

Completing the square:

(x + 4) ^2 - 16 = - 17

(x + 4) ^2 = - 1

x + 4 = + / - i

x = - 4 + i, - 4 - i.