We are given the polynomial f(x)=x^7 - x^6 - 11x^5 + 11x^4 + 19x^3 -1 9x^2 - 9x + 9 (f) Describe the Factor Theorem. Using this theorem show that f(x)= (x4 - 10x2 + 9) g(x) (g) Using long division, find g(x). Show all your work. (h) Calculate the following values: g(-1): g(1) (i) Using the Factor Theorem and synthetic division, factor g(). Show all your work (j) Describe the multiplicity of all the zeros of f(x), and describe the behavior of the graph of f(x) at these zeros (i.e., is the graph crossing the x-axis at these zeros or touches and turns around?). (k) Without graphing the function, and based solely on the degree of the polynomial, what is the maximum number of turning points that f(x) can have? (L) Graph f(x). How many turning points does it really have? Explain why the function has this number of turning points