Algebra help: polynomials and polynomial functions

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Polynomials and Polynomial Functions Unit Test 12/16/15, 3:01 PM Polynomials and Polynomial Functions Unit Test Luigi Gjurashaj is taking this assessment. 1. (1 point) Which equation is best represented by the graph above? (x + 1)(x – 3)(x + 2) (x – 1)(x + 3)(x + 2) (x – 1)(x – 3)(x + 2) (x + 1)(x + 3)(x – 2) 2. The graph of is shown below. (1 point) https://www.connexus.com/content/render.aspx?disableAssessment=…ebuser=1808734&page=1&header=true&idUnit=30173&idLesson=340080 Page 1 of 13 Polynomials and Polynomial Functions Unit Test 12/16/15, 3:01 PM What are the apparent zeros of the function graphed above? {–1, 2.5} {–17, 5} {–4, 0, 2} {–2, 0, 4} 3. What is a polynomial function in standard form with zeroes 1, 2, –3, and –1? (1 point) g(x) = x4 + x3 – 7x2 – x + 6 g(x) = x4 + x3 + 7x2 – x + 6 g(x) = x4 + x3 – 7x2 – x – 6 g(x) = x4 – x3 – 7x2 – x + 6 4. What are the zeros of the function? What are their multiplicities? (1 point) f(x) = 5x3 – 5x2 – 30x The numbers 3, –2, and 0 are zeros of multiplicity 1. The numbers 3, –2, and 0 are zeros of multiplicity 2. The numbers –3, 2, and 0 are zeros of multiplicity 1. The numbers –3, 2, and 0 are zeros of multiplicity 2. 5. What are the real and complex solutions of the polynomial equation? (1 point) x3 – 8 =0 1+i , and 1 – i 2, –1 + i 2, 1 + 2i 2, 2 +2i , and –1 – i , and 1 – 2i , and 2 – 2i 6. Which is equivalent to the following expression? (1 point) https://www.connexus.com/content/render.aspx?disableAssessment=…ebuser=1808734&page=1&header=true&idUnit=30173&idLesson=340080 Page 2 of 13 Polynomials and Polynomial Functions Unit Test 12/16/15, 3:01 PM 6. Which is equivalent to the following expression? (1 point) (2x2 + 4xy – y2) + (x2 + 3xy – y2) 3x2 – 7xy – 2y2 3x4 + 7xy – 2y4 3x2 + 7xy – 2y2 2x2 – 7xy + 2y2 7. Which is a factored form of 8x3 + 27? (1 point) (2x + 3)(2x + 3)(2x + 3) (2x + 3)(4x2 – 6x + 9) (2x – 3)(4x2 + 6x + 9) (2x – 9)(4x2 + 18x +81) 8. Divide –3x3 – 4x2 + 4x +3 by x – 2. (1 point) –3x2 + 2x + 24 –3x2 – 10x – 16, R – 29 –3x2 – 10x – 16 –3x2 + 2x + 24, R 35 9. Find the roots of the polynomial equation. (1 point) x3 – 2x2+ 10x + 136 = 0 –3 5i, –4 3 5i, –4 –3 i , 4 3 i, 4 10. Which correctly describes the roots of the following cubic equation? (1 point) x3 – 5x2 + 3x + 9 = 0 Three real roots, each with a different value One real root and two complex roots Three real roots, two of which are equal in value https://www.connexus.com/content/render.aspx?disableAssessment=…ebuser=1808734&page=1&header=true&idUnit=30173&idLesson=340080 Page 3 of 13 Polynomials and Polynomial Functions Unit Test 12/16/15, 3:01 PM Two real roots and one complex root 11. What is the second term of (m + n)5? (1 point) 125m4n 25m4n 25m4 5m4n 12. One zero of f(x) = x3 – 2x2 – 5x + 6 is 1. What are other zeros of the function? (1 point) 3 and –2 –3 and 2 1 and 2 1 and –3 13. Which of the following quartic functions has x = –1 and x = –3 as its only two real zeros? (1 point) y = x4 – 4x3 – 4x2 – 4x – 3 y = –x4 + 4x3 + 4x2 + 4x + 3 y = x4 +4x3 + 3x2 + 4x – 4 y = x4 + 4x3 + 4x2 + 4x + 3 14. Work Pad (2 points) Note: Remember to show all of the steps that you use to solve the problem. You can use the comments field to explain your work. Your teacher will review each step of your responses to questions 13–19 to ensure you receive proper credit for your answers. The design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 6 inches. If the length must be 1.5 times the height, what should each dimension be? Hint: Let x represent one of the dimensions, and then define the other dimensions in terms of x. https://www.connexus.com/content/render.aspx?disableAssessment=…ebuser=1808734&page=1&header=true&idUnit=30173&idLesson=340080 Page 4 of 13 Polynomials and Polynomial Functions Unit Test Select attachment 12/16/15, 3:01 PM or drag and drop a file into this area - 20 MB limit 15. https://www.connexus.com/content/render.aspx?disableAssessment=…ebuser=1808734&page=1&header=true&idUnit=30173&idLesson=340080 Page 5 of 13 Polynomials and Polynomial Functions Unit Test What are the real and complex solutions of the polynomial equation? 12/16/15, 3:01 PM (2 points) x4 – 41x2 = –400 Select attachment or drag and drop a file into this area - 20 MB limit https://www.connexus.com/content/render.aspx?disableAssessment=…ebuser=1808734&page=1&header=true&idUnit=30173&idLesson=340080 Page 6 of 13 Polynomials and Polynomial Functions Unit Test 12/16/15, 3:01 PM 16. Use synthetic division to find (–3) for ( ) = 4 – 2 3 – 4 + 4. (2 points) P Px x x x Select attachment or drag and drop a file into this area - 20 MB limit 17. https://www.connexus.com/content/render.aspx?disableAssessment=…ebuser=1808734&page=1&header=true&idUnit=30173&idLesson=340080 Page 7 of 13 Polynomials and Polynomial Functions Unit Test Find all the zeroes of the equation. 12/16/15, 3:01 PM (2 points) x4 – 6x2 – 7x – 6 = 0 Select attachment or drag and drop a file into this area - 20 MB limit https://www.connexus.com/content/render.aspx?disableAssessment=…ebuser=1808734&page=1&header=true&idUnit=30173&idLesson=340080 Page 8 of 13 Polynomials and Polynomial Functions Unit Test 12/16/15, 3:01 PM 18. Use Pascal’s triangle to expand the binomial. (2 points) (d – 5y)6 Select attachment or drag and drop a file into this area - 20 MB limit https://www.connexus.com/content/render.aspx?disableAssessment=…ebuser=1808734&page=1&header=true&idUnit=30173&idLesson=340080 Page 9 of 13 Polynomials and Polynomial Functions Unit Test 19. What is the equation of = 3 with the given transformations? y x vertical compression by a factor of , horizontal shift 8 units to the left, reflection across the 12/16/15, 3:01 PM (2 points) x-axis Select attachment or drag and drop a file into this area - 20 MB limit https://www.connexus.com/content/render.aspx?disableAssessment…ebuser=1808734&page=1&header=true&idUnit=30173&idLesson=340080 Page 10 of 13 Polynomials and Polynomial Functions Unit Test 20. What are all the real zeroes of y = (x –12)3 – 7? Select attachment 12/16/15, 3:01 PM (2 points) or drag and drop a file into this area - 20 MB limit Essay https://www.connexus.com/content/render.aspx?disableAssessment…ebuser=1808734&page=1&header=true&idUnit=30173&idLesson=340080 Page 11 of 13 Polynomials and Polynomial Functions Unit Test 12/16/15, 3:01 PM Note: Your teacher will grade your response to ensure you receive proper credit for your answer. 21. Explain how to find the degree of a polynomial. (2 points) 22. Can you always use synthetic division for dividing polynomials? Explain. (2 points) 23. If 2 + is a polynomial root, name another root of the polynomial, and explain how you know it must also be a root. (2 points) 24. How can you quickly determine the number of roots a polynomial will have by looking at the equation? (2 points) https://www.connexus.com/content/render.aspx?disableAssessment…ebuser=1808734&page=1&header=true&idUnit=30173&idLesson=340080 Page 12 of 13 Polynomials and Polynomial Functions Unit Test 25. Is a power function? Explain your reasoning. 12/16/15, 3:01 PM (2 points) © 2015 Connections Education LLC. https://www.connexus.com/content/render.aspx?disableAssessment…ebuser=1808734&page=1&header=true&idUnit=30173&idLesson=340080 Page 13 of 13
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