Unit 5 Evaluation. Multiple-Choice. Evaluation 05 Second Year Algebra 1 (MTHH ) Name I.D. Number

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1 Name I.D. Number Unit Evaluation Evaluation 0 Second Year Algebra (MTHH ) This evaluation will cover the lessons in this unit. It is open book, meaning you can use your textbook, syllabus, and other course materials. You will need to understand, analyze, and apply the information you have learned in order to answer the questions correctly. To submit the evaluation by mail, follow the directions on your Enrollment Information Sheet. To take the evaluation online, access the online version of your course; use the navigation panel to access the prep page for this evaluation and follow the directions provided. Note: A graphing calculator may be used on unit evaluations. You may also use scratch paper to work out the solutions. Multiple-Choice Select the response that best completes the statement or answers the question.. Which expression is a cubic polynomial? a. x 3 b. 3x + 3 c. x + 3x d. 3x. Which expression is a binomial? a. x b. x c. 3x + x + 4 d. x 9 3. What is the degree of the polynomial x + 4x + 3x 3 x? a. b. c. 3 d Which expression is equivalent to x 4 3x + 6? a. (x 4 x + 3) (x 4 x 9) b. x 4 3(x + 6) c. (3x 4 x + 3) + (3 x x 4 ) d. x(x 3 3x) + 6 Unit Evaluation MTHH 039

2 . Which expression is the factored form of x 3 + x x 6? a. (x + )(x + )(x 6) b. (x + )(x )(x 6) c. (x + 3)(x + )(x ) d. (x 3)(x )(x + ) 6. What are the zeros of the polynomial function y = (x 3)(x + )(x )? a.,, 3 b.,, 3 c. d. 3,,, 3, 7. Which polynomial function has zeros at 4, 3, and? a. f(x) = (x + 4)(x + 3)(x + ) b. g(x) = (x + 4)(x 3)(x ) c. h(x) = (x 4)(x 3)(x ) d. k(x) = (x 4)(x + 3)(x + ) 8. What is the remainder when x x + 7 is divided by x +? a. 3 b. c. d Which binomial is not a factor of x 3 x 7x? a. x b. x + c. x + 3 d. x + 0. Which of the following, when multiplied by x, results in a cubic polynomial whose standard form has three terms? a. (x ) b. x x c. x d. x Unit Evaluation MTHH 039

3 . Which expression is a factor of x 4 8x + 8? a. x 9 b. x + 6x 9 c. x 6x 9 d. x + 9. Which value is not a solution of x 4 3x 4 = 0? a. 3 b. 3 c. 3i d. i 6 3. A fourth-degree polynomial with integer coefficients has zeros at and 3 + Which number cannot also be a zero of this polynomial?. a. b. 3 c. 3 d Three roots of a fourth-degree polynomial equation with rational coefficients are + 3 a. 7 b. +, 7, and 4 c. 4 d Which number is also a root of the equation?. Two roots of a cubic polynomial equation with real coefficients are 3 and 4i. If the leading coefficient of the polynomial is, what is the equation? a. x 3 3x + 6x 48 = 0 b. x 3 3x 6x + 48 = 0 c. x 3 + 3x + 6x + 48 = 0 d. x 3 + 3x 6x 48 = 0 6. Which number is a root of f(x) = x 3 + 6x + 9x that has a multiplicity of? a. 3 b. c. 0 d. 3 Unit Evaluation MTHH 039

4 7. Three roots of a polynomial equation with real coefficients are 3, 3i, and 3i. Which of the following numbers must also be a root of the equation? a. + 3i only b. 3 and + 3i only c. + 3i and 3i only d. 3, + 3i, and 3i 8. One root of the equation x 3 + x = 0 is. What are the other two roots? a. ± i b. ± i c. ± + i d. ± i 9. A polynomial with real coefficients has 3, i, and i as three of its zeros. What is the least possible degree of the polynomial? a. 3 b. 4 c. d How many times does the graph of x cross the x-axis? a. 0 b. c. d. 4. Find the value of 7!. a. 04 b. 7 c. 040 d. 4. What is the value of 6! 8!? a. b. c. d Unit Evaluation MTHH 039

5 3. What is the value of 7 C? a. 7 b. c. 4 d Find the value of (3 + )! (4 )!. a. 3 b. 0 c. 8 d. 0. How many ways are there to select books from a collection of 7 books? a. b. 67 c. 7 d What is the expanded form of (a b) 3? a. a 3 + a b + ab + b 3 b. a 3 + 3a b + 3ab + b 3 c. a 3 a b + ab b 3 d. a 3 3a b + 3ab b 3 7. What is the third term in the expansion of (a b) 7? a. a b b. 7a 6 b c. 7a 6 b d. a b 8. What is the coefficient of the third term in the expansion of (a b)? a. 80 b. 3 c. 40 d Which term in the expansion of (a 3b) 6 has coefficient 60? a. second term b. third term c. fourth term d. fifth term Unit Evaluation MTHH 039

6 30. Which of the following is a factor of x 4 + x 3 3x 4x + 4? a. x + only b. x only c. x + and x d. x and x + 3. What are the solutions of x 3 + 4x + x 6 = 0? a.,, 3 b.,, 3 c.,, 3 d.,, 3 3. Find 3 P 3 C? a. b. 3 c. 4 d. 33. What is the coefficient of a b 3 in the expansion of (a + b)? a. 0 b. c. d The equation a 3 b 3 = (a b)(a + ab + b ) is used to find the. a. sum of cubes b. difference of cubes c. irrational roots d. degree of a polynomial 3. x = b b 4ac a is a. a. Polynomial function b. Quadratic Formula c. Quadratic equation d. Rational function 36. Classify 4x 3 x x by degree and by number of terms. a. cubic binomial b. quadratic binomial c. quadratic trinomial d. cubic trinomial Unit Evaluation MTHH 039

7 37. Write 3x (x 3 4x ) in standard form. Then classify by degree and by number of terms. a. x x 4 ; quadratic binomial b. 6x 6 7x 4 ; quintic binomial c. x 3 x ; cubic binomial d. 6x x 4 ; quintic binomial 38. Write y = (x 6)(x 4)(x + ) in standard form? a. y = x b. y = x 3 8x + 4x + 48 c. y = x 3 x + 4x 8 d. y = x 3 8x 8x Write a polynomial in standard form with zeros,, and. a. x 3 x + 3x 0 = 0 b. x 3 4x + 7x + 0 = 0 c. x 3 + x 3x + 0 = 0 d. x 3 + 6x 3x + 0 = Use synthetic division and the remainder theorem to find P( ) if P(x) = x 4 + x 3 8x 8x 9. a. 4 b. c. 6 d. none of these 4. Which polynomial is not a factor of 3x 4 6x 3 3x + 36x + 0? a. x b. x c. x + d. 3x + 4. Factor 3c a. 3(c + )(c c + ) b. 3(c + )(c c + ) c. (c + )(c c + ) d. (c )(c c + ) Unit Evaluation MTHH 039

8 43. Use the rational root theorem to determine all possible rational roots of x 3 + 4x + 4x + 0 = 0. Do not find the actual roots. a. ±,, 0,, b. ±,,, 0,, c. ± 0,,,, d. ±,, 0, 0,,,, One root of the polynomial equation 0 = x 3 x 4x + 30 is + i. Find an additional root. a. + i b. + i c. + i d. i 4. Which polynomial function does NOT have 0 as a root? a. f(x) = x 4 b. h(x) = x 4 + 3x x c. k(x) = x x 3 d. g(x) = x 3x 46. Which polynomial function has the most roots? a. g(n) = n 3 + 3n 6 b. f(a) = a 4 + a 3 3a c. g(m) = 8m d. f(x) = x 47. Evaluate 9! 6!? a. 304 b. 60,480 c. 04 d. 84 Unit Evaluation MTHH 039

9 48. There are 7 students participating in a spelling bee. How many ways can students who go first and second be chosen? a. 36 ways b. 7,0 ways c. 7 ways d. 7 ways 49. Use Pascal s Triangle to expand (3a b) 4. a. 8a 4 08a 3 b + 4a b ab 3 + b 4 b. 8a 4 a 3 b + 8a b ab 3 + b 4 c. 8a a 3 b + 4a b + ab 3 + b 4 d. 8a 4 + a 3 b + 8a b + ab 3 + b 4 0. A salad bar offers 0 choices of toppings for lettuce. In how many ways can you choose three or four toppings? a. 0 b. 330 c. 0 d. 70 Carefully check your answers on this evaluation and make any corrections you feel are necessary. When you are satisfied that you have answered the questions to the best of your ability, transfer your answers to an answer sheet. Please refer to the information sheet that came with your course materials. Unit Evaluation MTHH 039

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