Answer: A: -2x^3 - 6x^2 + 9x
Step-by-step explanation:
f(x) - g(x) is a simple subtraction problem, just like 2 - 1, or 8 - 5. So, treat the functions like normal questions.
> f(x) = 3x^3 - 4x^2 + 6x
> g(x) = 5x^3 + 2x^2 - 3x
> f(x) - g(x)
Substitute these values for f(x) and g(x).
> f(x) - g(x)
> (3x^3 - 4x^2 + 6x) - (5x^3 + 2x^2 - 3x)
Now, we combine like terms*:
> For x^3: (3x^3 - 5x^3) = -2x^3
> For x^2: (-4x^2 - 2x^2) = -6x^2
> For x: (6x + 3x) = 9x
*NOTE: Remember that when there is a subtraction sign in front of a group of numbers, all the numbers inside of the parenthesis are multiplied by -1, and get their signs switched.
Putting all of these values together, we get (-2x^3 - 6x^2 + 9x).
