Example Question - function multiplication

Multiplication of Two Functions

The question asks for the multiplication of two functions f(x) and g(x), where: f(x) = 2x + 5 g(x) = x^2 - 5x To find the product (f * g)(x), you multiply each term in f(x) by each term in g(x): (f * g)(x) = (2x + 5)(x^2 - 5x) Now expand the product: = 2x * x^2 + 2x * (-5x) + 5 * x^2 + 5 * (-5x) = 2x^3 - 10x^2 + 5x^2 - 25x = 2x^3 - (10x^2 - 5x^2) - 25x = 2x^3 - 5x^2 - 25x Therefore, the result is: (f * g)(x) = 2x^3 - 5x^2 - 25x This polynomial is already in its simplest form.