Final answer:
To find the product of the functions f(x) and g(x), you multiply each term of f(x) by each term of g(x), combine like terms, and express the result as a polynomial. The final simplified form of the product f(x)*g(x) is x³ - 12x² + 45x - 54.
Step-by-step explanation:
To find the product of the functions f(x) and g(x), denoted as f(x)*g(x), you simply need to multiply the two functions together. Given f(x) = x² - 9x + 18 and g(x) = x - 3, we first apply the distributive property to multiply each term in f(x) by each term in g(x).
The multiplication process is as follows:
- (x²) * (x) = x³
- (x²) * (-3) = -3x²
- (-9x) * (x) = -9x²
- (-9x) * (-3) = 27x
- (18) * (x) = 18x
- (18) * (-3) = -54
Next, we combine like terms:
- x³ is the only cubic term.
- -3x² and -9x² combine to -12x².
- 27x and 18x combine to 45x.
- And we have a constant term of -54.
Putting it all together, the product f(x)*g(x) can be expressed as a polynomial in simplest form:
x³ - 12x² + 45x - 54