Answers to Questions on Polynomial Functions


  1. Question: What is the degree of the polynomial 2 x9 + 7 x3 + 191?

    Answer: 2 x9

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  2. There are (infinitely) many right answers to these questions.
    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 Explain

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

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

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  3. Question: What is the largest number of real roots that a 7th degree polynomial could have? What is the smallest?

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

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  4. Question: How many real roots can a fourth degree polynomial have?

    Answer: 0 to 4, inclusive. Explain

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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 Explain

    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 Explain

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

      Answer: -5, 0, and 2 Explain

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

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

    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 Explain

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  5. Question: Are you interested in questions involving watermelons?

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

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