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Polynomial Standard Form and Factorization Review

Understand polynomial standard form representation, factorization, end behavior, zeros multiplicity, division methods, error analysis, and roots relationship in a comprehensive review.

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Polynomial Standard Form and Factorization Review

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  1. Chapter 6Review

  2. Write the polynomial in standard form.

  3. Write the polynomial in standard form.

  4. Write the polynomial in standard form.

  5. Write the polynomial in standard form.

  6. Name by degree and by number of terms.

  7. Name by degree and by number of terms. • By degree – Cubic • By number of terms - Trinomial

  8. Name by degree and by number of terms..

  9. Name by degree and by number of terms.. • By degree – Quartic • By number of terms - Binomial

  10. Write the function in factored form.Determine the zeros and any multiplicity.

  11. Write the function in factored form.Determine the zeros and any multiplicity. The zeros are 0 (multiplicity 2), 5 and -2.

  12. Describe the end behavior of the function.

  13. Describe the end behavior of the function.

  14. Describe the end behavior of the function.

  15. Describe the end behavior of the function.

  16. Use the graph to approximate all relative minimums and maximums.

  17. Use the graph to approximate all relative minimums and maximums. Relative Maximum is 1. Relative Minimums are -7 and -1.5.

  18. Divide using long division.

  19. Divide using long division.

  20. Divide using synthetic division.

  21. Divide using synthetic division.

  22. Explain the error that was made in the following problem.

  23. Explain the error that was made in the following problem. The student forgot to insert a zero in the top line for the term that is missing.

  24. List the possible rational zeros.Do not find the zeros.

  25. List the possible rational zeros.Do not find the zeros.

  26. Given the roots of a polynomial to be -2 and -3i, you state the factors of the polynomial are (x+2) and (x+3i). Are you correct? Explain.

  27. Given the roots of a polynomial to be -2 and -3i, you state the factors of the polynomial are (x+2)(x+3i). Are you correct? Explain. No, if -3i is a root, then 3i must also be a root therefore the factors would be: (x+2)(x+3i)(x-3i)

  28. Find all solutions (real and imaginary).

  29. Find all solutions (real and imaginary).

  30. Find all solutions (real and imaginary).

  31. Find all solutions (real and imaginary).

  32. Good Luck on Monday and Tuesday.

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