Which statements are true about the polynomial function? f(x)=x3−x2−4x+4 select each correct answer. f(x)=0 when x=−1 . f(x) divided by (x−1) has a remainder of 0. (x−1) is a factor of f(x) . f(−1)=0

To determine which of the statement is/are true, we simply have to evaluate the given choices.

  a.   f(x) = 0 when x = -1

     f(x) = (-1)^3 - (-1)^2 - 4(-1) + 4
     f(x) = 6

  FALSE

   b. f(x) divided by x - 1 has a remainder of 0.

     f(x) = (1)^3 - (1)^2 - 4(1) + 4
     f(x) = 1 - 1 - 4 + 4 = 0

  TRUE.

   c. (x - 1) is a factor of f(x)

  Since, the division of f(x) by x - 1 gave an answer of zero this means that it is a factor. 

    TRUE.

   d. f(-1) = 0.

 In relation to letter a of this item, if we are to substitute -1 to x of the given equation, the answer is 6 instead of zero.