A student used synthetic division to divide [tex]x^{3}-3x^{2}+4[/tex] by [tex]x+1[/tex].


Original Student Answer:

1 -3 4

1 -2

1 -2 2

Answer: x-2, R = 2


a. Mark and explain where the error(s) occurred in the student's setup for synthetic division.


b. After marking the errors, correctly perform synthetic division.


c. Using the Remainder Theorem, is your answer and x+1 a factor of the polynomial [tex]x^{3}-3x^{2}+4[/tex]? If so, explain how you know.


d. If your answer to part c is yes, use the Factor Theorem to show the fully factored form of the polynomial [tex]x^{3}-3x^{2}+4[/tex]


Please go step-by-step and explain. Best/most helpful answer will be marked Brainliest <3