Note: enter your answer and show all the steps that you use to solve this problem in the space provided. f ( x ) = 9 x 3 + 2 x 2 − 5 x + 4 and g ( x ) = 5 x 3 − 7 x + 4 . what is f ( x ) − g ( x ) ? show all of your steps and write your final answer in factored form.

The answer is 4x³ + 2x² + 2x = 2x(2x² + x + 1)

Step-by-step explanation:

∵ f(x) = 9x³ + 2x² - 5x + 4

∵ g(x) = 5x³ - 7x + 4

∴ f(x) - g(x) = (9x³ + 2x² - 5x + 4) - (5x³ + 0 - 7x + 4)

                 = (9x³ - 5x³) + (2x² - 0) + (-5x + 7x) + (4 - 4)

                 = 4x³ + 2x² + 2x = 2x(2x² + x + 1)

- both graphs increase on their domain.

- the graphs of both functions have the same x-intercept.

- neither graph has a y-intercept.