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Polynomials and Polynomial Functions Unit Test 30/11/15 19:31 Polynomials and Polynomial Functions Unit Test Frank Gjurashaj is taking this assessment. Multiple Choice 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?disableAssessm…er=1393561&page=1&header=true&idUnit=30173&idLesson=340080 Page 1 of 13 Polynomials and Polynomial Functions Unit Test 30/11/15 19:31 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 Multiple Choice 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 , and –1 – i 2, 1 + 2i 2, 2 +2i , and 1 – 2i , and 2 – 2i 6. Which is equivalent to the following expression? (1 point) https://www.connexus.com/content/render.aspx?disableAssessm…er=1393561&page=1&header=true&idUnit=30173&idLesson=340080 Page 2 of 13 Polynomials and Polynomial Functions Unit Test 30/11/15 19:31 3p2 + 8pq – 3q2 4p2 + 8pq + q2 4p4 + 8pq – 3q4 4p2 + 8pq – 3q2 7. Which is a factored form of 216p3 + 125q3? (1 point) (6p + 5q)(36p2 + 30pq + 25q2) (6p + 5q)(36p2 – 30pq – 25q2) (6p + 5q)(36p2 + 30pq – 25q2) (6p + 5q)(36p2 – 30pq + 25q2) Multiple Choice 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 – 3x2 + 4x – 12 = 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 Two real roots and one complex root 11. What is the second term of (s + v)5? (1 point) 25s4 https://www.connexus.com/content/render.aspx?disableAssessm…er=1393561&page=1&header=true&idUnit=30173&idLesson=340080 Page 3 of 13 Polynomials and Polynomial Functions Unit Test 30/11/15 19:31 25s4v 5s4v 125s4v 12. One zero of f(x) = x3 + 2x2 – 5x – 6 is 2. What are other zeros of the function? (1 point) 1 and 3 –1 and –3 2 and –3 2 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?disableAssessm…er=1393561&page=1&header=true&idUnit=30173&idLesson=340080 Page 4 of 13 Polynomials and Polynomial Functions Unit Test Select attachment 30/11/15 19:31 or drag and drop a file into this area - 20 MB limit 15. What are the real and complex solutions of the polynomial equation? (2 points) x4 – 41x2 = –400 https://www.connexus.com/content/render.aspx?disableAssessm…er=1393561&page=1&header=true&idUnit=30173&idLesson=340080 Page 5 of 13 Polynomials and Polynomial Functions Unit Test Select attachment 30/11/15 19:31 or drag and drop a file into this area - 20 MB limit 16. Use synthetic division to find (–3) for ( ) = 4 – 2 3 – 4 + 4. (2 points) P Px x x x https://www.connexus.com/content/render.aspx?disableAssessm…er=1393561&page=1&header=true&idUnit=30173&idLesson=340080 Page 6 of 13 Polynomials and Polynomial Functions Unit Test Select attachment 30/11/15 19:31 or drag and drop a file into this area - 20 MB limit 17. Find all the zeroes of the equation. (2 points) x4 – 6x2 – 7x – 6 = 0 https://www.connexus.com/content/render.aspx?disableAssessm…er=1393561&page=1&header=true&idUnit=30173&idLesson=340080 Page 7 of 13 Polynomials and Polynomial Functions Unit Test Select attachment 30/11/15 19:31 or drag and drop a file into this area - 20 MB limit 18. Use Pascal’s triangle to expand the binomial. (2 points) (d – 5y)6 https://www.connexus.com/content/render.aspx?disableAssessm…er=1393561&page=1&header=true&idUnit=30173&idLesson=340080 Page 8 of 13 Polynomials and Polynomial Functions Unit Test Select attachment 30/11/15 19:31 or drag and drop a file into this area - 20 MB limit 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 (2 points) x-axis https://www.connexus.com/content/render.aspx?disableAssessm…er=1393561&page=1&header=true&idUnit=30173&idLesson=340080 Page 9 of 13 Polynomials and Polynomial Functions Unit Test Select attachment 30/11/15 19:31 or drag and drop a file into this area - 20 MB limit 20. What are all the real zeroes of = ( –12)3 – 7? (2 points) y x https://www.connexus.com/content/render.aspx?disableAssess…er=1393561&page=1&header=true&idUnit=30173&idLesson=340080 Page 10 of 13 Polynomials and Polynomial Functions Unit Test Select attachment 30/11/15 19:31 or drag and drop a file into this area - 20 MB limit Essay 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) https://www.connexus.com/content/render.aspx?disableAssess…er=1393561&page=1&header=true&idUnit=30173&idLesson=340080 Page 11 of 13 Polynomials and Polynomial Functions Unit Test 30/11/15 19:31 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?disableAssess…er=1393561&page=1&header=true&idUnit=30173&idLesson=340080 Page 12 of 13 Polynomials and Polynomial Functions Unit Test 25. Is 30/11/15 19:31 a power function? Explain your reasoning. (2 points) © 2015 Connections Education LLC. https://www.connexus.com/content/render.aspx?disableAssess…er=1393561&page=1&header=true&idUnit=30173&idLesson=340080 Page 13 of 13
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