Answer
$f(x) \cdot g(x) = 2x^3 - x^2 - 11x + 10$
$\text{The domain is the set of all real numbers.}$
Work Step by Step
This exercise asks us to multiply $f(x)$ and $g(x)$. Let's write out the problem:
$f(x) \cdot g(x) = (2x + 5)(x^2 - 3x + 2)$
Distribute terms first to get rid of the parentheses, paying attention to the signs:
$f(x) \cdot g(x) = (2x)(x^2) + (2x)(-3x) + (2x)(2) + (5)(x^2) + (5)(-3x) + (5)(2)$
Multiply out the terms:
$f(x) \cdot g(x) = (2x^3) + (-6x^2) + (4x) + (5x^2) + (-15x) + (10)$
Combine like terms:
$f(x) \cdot g(x) = 2x^3 - x^2 - 11x + 10$
When we find the domain, we want to find which values of $x$ will cause the function to become undefined; in other words, we want to find any restrictions for $x$. In this exercise, $x$ can be any real number since there are no restrictions, so the domain is all real numbers.
