✅ PreAssessment Polynomial Unit (30 Questions)
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Directions: Identify the choice that best completes the statement or answers the question.
1. Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms.
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The following polynomial corresponds with Question 2.
2. Write the polynomial above in standard form.
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3. Determine the degree of the following polynomial:
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4. Match the following expression with its name.
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5. What is the perimeter of the following figure?
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For questions 11 & 12, factor the polynomials.
11. Factor the following polynomial.
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12. Factor the following polynomial.
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13. Factor by grouping.
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14. Use a graphing calculator to determine which type of model best fits the values in the table.
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a. quadratic model, it has a constant 2nd difference
b. cubic model, it has a constant 3rd difference
c. linear model, it has a constant 1st difference
d. none of these
15. Use a graphing calculator to find the relative minimum, relative maximum, and zeros of the function below. If necessary, round to the nearest hundredth.
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a. relative minimum: (–62.24, 0.36), relative maximum: (37.79, –3.69), zeros: x = 5, –2, 2
b. relative minimum: (0.36, –62.24), relative maximum: (–3.69, 37.79), zeros: x = –5, –2, 2
c. relative minimum: (0.36, –62.24), relative maximum: (–3.69, 37.79), zeros: x = 5, –2
d. relative minimum: (–62.24, 0.36), relative maximum: (37.79, –3.69), zeros: x = –5, –2
16. Find the zeros of y = x(x − 3)(x − 2). Then graph the equation.
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a. 3, 2, –3
b. 0, –3, –2
c. 3, 2
d. 0, 3, 2
17. Write a polynomial function in standard form with zeros at 5, –4, and 1.
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18. Solve the polynomial.
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19. Evaluate the polynomial 6x − y for x = −3 and y = 2.
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20. For which values of m and n will the binomial below have a positive value?
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21. A fireworks company has two types of rockets called Zinger 1 and Zinger 2. The polynomial −16t²+ 150t gives the height in feet of Zinger 1 at t seconds after launch.The polynomial −16t²+ 165t gives the height of Zinger 2 at t seconds after launch. If the rockets are launched at the same time and both explode 6 seconds after launch,how much higher is Zinger 2 than Zinger 1 when they explode?
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22. Write a polynomial with zeros at 4, 2, and 1. Then graph the function.
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a. P(x) = (x− 4)(x+ 2)(x− 1)
b. P(x) = (x− 4)(x− 2)(x− 1)
c. P(x) = (x+ 4)(x− 2)(x+ 1)
d. P(x) = (x+ 4)(x+ 2)(x+ 1)
23. The ticket office at Orchestra Center estimates that if it charges x dollars for box seats for a concert, it will sell 50 − x box seats. The function S = 50x − x² gives the estimated income from the sale of box seats. Graph the function, and use the graph to find the price for box seats that will give the greatest income.
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24. Determine the number of real zeros possible for the polynomial,
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25. Using the following polynomial explain how the degree and leading coefficient will effect the end behavior.
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a. Because the degree is odd, the ends will point in opposite directions, and because the leading coefficient is negative the graph will increase from right to left.
b. Because the degree is odd, the ends will point in opposite directions, and because the leading coefficient is negative the graph will decrease from right to left.
c. Because the degree is odd, the ends will point in the same direction, and because the leading coefficient is negative the graph will increase from right to left.
d. Because the degree is odd, the ends will point in the same direction, and because the leading coefficient is negative the graph will decrease from right to left.
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27. Find the inverse of the following polynomial. Determine if the inverse is a function.
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28. Determine if the following is a function, then state the domain and range:
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This graphs is for question 29.
29. The graph above is a model of the polynomial to follow. Is the graph a function? What is the domain and range of the function?
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This graphs is for question 30.
30. The graph above is a model of the polynomial below. Is the inverse of this graph a function? Why?
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a. A Yes, it is a function. It passes the horizontal line test.
b. No, it is not a function. It fails the horizontal line test.
c. Yes, it is a function. It passes the vertical line test.
d. No, it is not a function. It fails the vertical line test.
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