Identify all of the root(s) of g(x) = (x2 + 3x - 4)(x2 - 4x + 29).

A product equals zero when at least one factor equals zero. The first factor, x² + 3x − 4, factors as (x + 4)(x − 1), giving roots −4 and 1. For x² − 4x + 29, the quadratic formula gives x = (4 ± √(−100))/2 = 2 ± 5i. Thus the roots are −4, 1, 2 + 5i, and 2 − 5i.

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