posted by Maddie .
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.
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.