Final answer:
The product of the functions g(x) = 4x + 1 and h(x) = x - 5 is calculated using the distributive property, resulting in 4x² - 19x - 5 after simplification. None of the provided answer options match this result.
Step-by-step explanation:
Calculating the Product of g(x) and h(x)
To find the product of the functions g(x) = 4x + 1 and h(x) = x - 5, we need to use the distributive property to multiply each term in g(x) by each term in h(x). Here are the steps for the multiplication:
Multiply the term 4x from g(x) by x from h(x) to get 4x².
Multiply the term 4x from g(x) by -5 from h(x) to get -20x.
Multiply the term 1 from g(x) by x from h(x) to get x.
Multiply the term 1 from g(x) by -5 from h(x) to get -5.
Now, we combine all the products: g(x) ⋅ h(x) = 4x² + x - 20x - 5, which simplifies to 4x² - 19x - 5.
However, none of the answer choices matches this result, so it seems there may be a typo in the options provided. Since the options show cubic terms and our multiplication did not result in any cubic terms, it's reasonable to suggest that the student rechecks the question or the provided answer choices.