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1. Consider the function f(x) = x3 + 7x2 + 2x - 40 .
a. Find the possible rational roots of f(x) = 0.
b. Use synthetic division to divide f(x) by x - 2. Show all your work. Use your answer to explain whether or not x – 2 is a factor of f(x).
c. Factor f(x) completely. Show all your work.
d. Sketch the graph of f(x) by plotting the x-intercepts, finding and plotting additional points on the graph, and using what you know about the graph’s end behavior.

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  1. Why don't you start with b)
    You would see that the division is exact , thus x-2 is a factor
    Your synthetic division should have a result of x^2 + 9x + 20

    so it fully factors to (x-2)(x+5)(x+4)
    Once factored, the roots are simple to see.

    btw, the order of the questions is poorly presented,
    question a) and c) should be interchanged.

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