Answers to Questions on Polynomial Functions

Answer: 2 x⁹

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1. Question: What is an example of a 3rd degree polynomial?
   

   Answer: Any polynomial whose highest degree term is x³. Examples are 5 x³ and -x³ + 2x² - 1

2. Question: What is an example of a 5th degree polynomial with exactly 3 terms?
   

   Answer: An example is 2x⁵ - 2x² - 10x

3. Question: What is an example of a 4th degree polynomial with exactly 4 terms?
   

   Answer: An example is -x⁴ - x³ + 3x + 2

Answer: A seventh degree polynomial has at least one and at most 7 real roots.

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Answer: 0 to 4, inclusive.

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1. Question: What is the large scale behavior of f(x) = -x⁶+ ax⁵ + bx⁴+ cx³+ dx²+ ex + g?
   

   Answer: As x becomes very large positive or very large negative f(x) becomes more and more negative.

2. Question: What is the large scale behavior of f(x) = x⁵ + ax⁴+ bx³+ cx²+ dx + e?
   

   Answer: As x gets large and negative, f(x) becomes large and negative. As x gets large and positive, f(x) becomes very large and positive.

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1. Question: What are the roots of g(x) = 3x² - 7x - 20?
   

   Answer: -5/3 and 4

2. Question: What are the roots of h(x) = x² - 4 x + 12?
   

   Answer: complex roots: 2 + 2 sqrt(2) i, and 2 - 2 sqrt(2) i

3. Question: What are the roots of f(x) = 2x³ + 6x² - 20x?
   

   Answer: -5, 0, and 2

4. Question: What are the roots of f(x) =x³ - x² - 5x + 5?
   

   Answer: 1, sqrt(5), -sqrt(5)

5. Question: What are the roots of p(x) = x³ + 3x² + 3x + 2?
   

   Answer: real root: -2, complex roots: -1/2 + (sqrt(3)/2)i, and -1/2 - (sqrt(3)/2)i

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Answer: Here's a hint: How much of the original load of watermelon was not water?

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