Which of the following is the complete list of roots for the polynomial function f of x is equal to open paren x squared plus 6 x plus 8 close paren times open paren x squared plus 6 x plus 13 close paren ?

Set each factor equal to zero. The first factor, x² + 6x + 8, factors as (x + 2)(x + 4), giving roots −2 and −4. For the second factor, x² + 6x + 13 = 0, the quadratic formula gives x = (−6 ± √(36 − 52))/2 = −3 ± 2i. Thus the complete list is −2, −4, −3 + 2i, and −3 − 2i, which is choice D.

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