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Polynomials True or False

1. According to Descartes Rule of signs, which of the following is true of the polynomial f(x) = x3 + 2x2 – x – 2? -> It may have one positive root and two negative roots.
2. According to Descartes Rule of signs, which of the following is true of the polynomial f(x) = x4 + x3 – 2x2 – x – 2? -> It may have two real roots and two complex roots.
3. Which of these is an upper bound for -> x = 4
4. Which of these is a lower bound for y = x3 + 4x2? -> None of them
5. A polynomial goes through the points (2, -1) and (4, 3). What do we know for sure about the polynomial's zeros? -> The polynomial has a zero at x = 3.
6. How does the graph of y = (x − 3)3(x + 3)2 change around x = 3, from left to right? -> It changes from negative to positive.
7. How does the graph of y = (x – 1)4(x + 5)4(x + 1)4 change around x = -5, from left to right? -> It starts positive and stays positive.
8. How does the graph of y = (x – 1)(x + 5)(x + 1) change around x = -5, from left to right? -> It changes from negative to positive.
9. How does the graph of y = -(x – 1)2(x + 1)7 change around x = 1, from left to right? -> It starts negative and stays negative.
10. What are the roots of y = x3 + 2x2 – 4x – 8? -> x = -2 and ±2i

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