Which of the following is a factor of f (x) = 5x3 + 24x2 - 75x + 14? A. (x + 1 over 2) B. (x - 1 over 2) C. (x + 2) D. (x - 2)

F (x) = 5x³ + 24x² - 75x + 14

Set each given factor equal to 0 and obtain 4 values of x:

A) x = - 1/2

B) x = 1/2

C) x = - 2

D) x = 2

Now, use the hit and trial method to find the answer. We are looking for a value of x which will put f (x) = 0

5 (-1/2) ³ + 24 (-1/2) ² - 75 (-1/2) + 14

= / = 0

5 (1/2) ³ + 24 (1/2) ² - 75 (1/2) + 14

= / = 0

5 (-2) ³ + 24 (-2) ² - 75 (-2) + 14

= / = 0

5 (2) ³ + 24 (2) ² - 75 (2) + 14

= 0

Thus, the answer is D