1.(a) Use the Fundamental Theorem of Algebra to determine the number of complex roots 2x ^ 2 + 3x + 5 1 ) (b) What are the roots of 2x ^ 2 + 3x + 5 Show your work. (8 total points - 1 point for each corroct answorpoints for showing/explaining ALL of your work, including an explanation of why you chose the method you used to the roots)

2. Consider the function f(x) = x ^ 3 - 2x ^ 2 + 3 (a) Factor the function completely. any complex factors if they exist. (1 point for correct answer, 4 points for showing/explaining all work) (b) Draw a sketch of the function. Your sketch should not be perfect (because you should NOT use outside resources) but must have the correct general shape (1 point), show the correct end behavior (1 point), and show the correct x- and y intercepts (2 points )

3. Complete the following operation using both long division and synthetic division. (x ^ 3 + 5x ^ 2 + 7x - 12) divided by (x - 2) Show your work Long Division (1 point for correct answer, 4 points for all correct work/steps shown) Synthetic Division : (1 point for correct answer , 3 points for all correct work/steps shown ):