Question

Given that f(x) = x^2 - 9x + 18 and g(x) = x - 3 , find f(x) . g(x) \) and express the result as a polynomial in the simplest form.

a) x^3 - 12x^2 + 45x - 54
b) x^3 - 6x^2 - 9x + 54
c) x^3 - 12x^2 + 45x - 36
d) x^3 - 6x^2 - 9x + 36

Answer 1

To find the product of f(x) and g(x), multiply each term in f(x) with each term in g(x) and simplify the expression.

Step-by-step explanation:

To find the product of f(x) and g(x), we need to multiply the two functions together by multiplying each term in f(x) with each term in g(x).

f(x) = x^2 - 9x + 18 and g(x) = x - 3.
Multiplying f(x) and g(x) gives: f(x) * g(x) = (x^2 - 9x + 18) * (x - 3)

Simplifying the expression, we get: f(x) * g(x) = x^3 - 12x^2 + 45x - 54.