Consider the function f(x) = x³ − 13x² +44x − 32. a. use the fact that x − 4 is a factor of f to factor this polynomial. b. find the x-intercepts for the graph of f. c. at which x-values can the function change from being positive to negative or from negative to positive? d. to sketch a graph of x, we need to consider whether the function is positive or negative on the four intervals x < 1, 1 < x < 4, 4 < x < 8, and x > 8. why is that? e. how can we tell if the function is positive or negative on an interval between x-intercepts? f. for x < 1, is the graph above or below the x-axis? how can you tell? g. for 1 < x < 4, is the graph above or below the x-axis? how can you tell? h. for 4 < x < 8, is the graph above or below the x-axis? how can you tell? i. for x > 8, is the graph above or below the x-axis? how can you tell?