Algebra 2

Use the following equation to perform the operations below (do not graph the equation yet):
y ={x + 5}{x + 1}\{(x + 3)(x - 2)}{(x - 4)(x + 1)}) - {1}/{x - 2}

What graphical feature occurs at {x} = -1? Use the "trace" function, zoom in on the graph, or look at a table of values to verify what is happening at {x} = -1. Why isn't there a vertical asymptote at {x} = -1?
c. Solve the equation for {x}when y = 0}
find the roots of the equation. Show all of your work and explain the strategies you use in each step.

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  1. $f(x) = x^{5} - 3x^{4} - 5x^{3} + 5x^{2} - 6x + 8$

    b. Identify all possible rational zeros.
    c. How many possible positive real zeros are there? How many possible negative real zeros? How many possible complex zeros?
    d. Graph the polynomial to approximate the zeros. What are the rational zeros? Use synthetic division to verify these are correct.
    e. Write the polynomial in factor form.
    f. What are the complex zeros?

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