Answer
$f(x) • g(x) = x^3 - 4x^2 - 16x + 64$
The domain is all real numbers because $x$ can be any real number.
Work Step by Step
In this problem, we are asked to multiply two functions.
Let us go ahead and set up the multiplication problem, separating the two functions with parentheses:
$f(x) • g(x) = (x - 4)(x^2 - 16)$
Use the FOIL method to expand the binomial. We will multiply the first terms, the outer terms, the inner terms, and the last terms:
$f(x) • g(x) = (x)(x^2) - 16(x) - 4(x^2) - (4)(-16)$
Multiply the terms out to simplify:
$f(x) • g(x) = x^3 - 16x - 4x^2 + 64$
Let us put the terms in order from the term with the greatest degree to that with the smallest degree:
$f(x) • g(x) = x^3 - 4x^2 - 16x + 64$
The domain is all real numbers because $x$ can be any real number.
