Long and Synthetic Division

Information For questions 1 - 4, f (x) = 4x3 - 3x2 - 4x + 3 is divided by x - 2 and the synthetic division is shown below. 2 4 -3 -4 3 8 10 12 5 6 15 Question 1 Using the remainder theorem, we can conclude that f(2) = Not yet answered Select one: Points out of O a. 4 10.00 O b. 5 O c. 3 O d. 15Question 2 According to the rational zero theorem, if the rational number p/q is a zero of f(x), then p is a factor of Not yet answered Select one: Points out of O a. 4 10.00 O b. 5 O C. 3 O d. 15 Question 3 According to the rational zero theorem, if the rational number p/q is a zero of f(x), then q is a factor of Not yet answered Select one: Points out of O a. 4 10.00 O b. 5 O c. 3 O d. 15Question 4 Which of the following statements are true? Not yet answered Select one: Points out of O a. Using the factor theorem, we can conclude that x - 2 is a factor of f(x). 10.00 O b. Using the factor theorem, we can conclude that x - 2 is not a factor of f(x). O c. Using the factor theorem, we can conclude that x + 2 is a factor of f(x). O d. Using the factor theorem, we can conclude that x + 2 is not a factor of f(x).Information For questions 5 - 6, f(x) = 2x3 - 9x2 + 13x- 6. Question 5 Use the rational zero theorem to drag and drop the values below to list the possible rational zeros of f(x) = 2x3 - 9x2 + 13x - 6. Not yet answered Possible Factors of Points out of Rational : 10.00 Zeros Factors of 1 2 3 4 5 -6 6 Question 6 Use the information from above to find all the zeros of f(x) = 2x3 + 3x2 - 5x - 6. The zeros of f(x) = 2x3 + 3x2 - 5x - 6 are Not yet answered Select one: Points out of 10.00 O a. x= -1, X= 1, X= N / - N/ W O b. * = - 2, X = 4, X= O C. * = - 2, X= - 1, X= W / N Od. x = 1, X = 2, X= N / W Pre-Lakuus A[(V/ CV_ IF 31Question 7 (x4 + 6x3 + 7x2 + 12x- 3) + (x+3) Not yet answered Points out of 10.00 x + + 1 -1 2 -2 3 -3 +3 4 -15 15 -48 48 42 -57 X +3 X - 3 18 Question 8 (6x2 + 11x-43) + (3x-5) Not yet answered Points out of 10.00 x + 1 -2 2 -7 +7 -13 13 -8 8 3x + 5 3x - 5Question 1 Not yet answered Points out of 11.12 Question 2 Not yet answered Points out of 11.11 Christian travels from a location in lndio, California that has an elevation of 20 feet below sea level to a second location with an elevation of 1 3 feet above sea level. Christian travels on a continuous road and his trip can be modeled bya polynomial function with time in minutes on the xaxis and elevation in feet on the yaxis. Which of the following statements must be true? Select one: 0 a. Christian's elevation was at 0 feet at some time during his trip. 0 b. Christian's elevation increased at a constant rate. O c Christian's trip took 7 minutes. 0 d. Christian's elevation was never less than 20 feet below sea level or more than 13 feet above sea level during his trip. Charles evaluated a function fat x= 4 and x= 5. He found that f(4) = 7 and f(5) = 2. What conclusion can Charles make? Select one: 0 a. Charles can use the Intermediate Value Theorem to conclude that there is a zero between 2 and 7. O b. Charles can use the Intermediate Value Theorem to conclude that there is a zero between 5 and 2. O c. Charles can use the Intermediate Value Theorem to conclude that there is a zero between 5 and 4. 0 d. There is not enough information to draw a conclusion Question 3 Ciara evaluated a function fat x = 4 and x = 5. She found that f(4) = 2 and f(5) = 7. What conclusion can Ciara make? Not yet answered Select one: Points out of O a. Ciara can use the Intermediate Value Theorem to conclude that there is a zero between 2 and 7. 11.11 O b. Charles can use the Intermediate Value Theorem to conclude that there is a zero between 4 and 5. O c. Charles can use the Intermediate Value Theorem to conclude that there is a zero between 4 and 7. O d. There is not enough information to draw a conclusion.Information For questions 4 - 9, Carter wants to find the zeros of the polynomial function below. f(x) = 2x3 - 3x2 -9x+10 Question 4 Drag and drop the values to list the possible rational zeros from low to high, disregarding the + symbols. For whole numbers, Not yet enter 1 as the denominator. answered Points out of + 11.11 2 3 4 5 6 9 10 12 15 18 20 30Question 5 Use synthetic division to find f(2). Not yet answered Select one: Points out of O a. 6 11.11 O b. -4 O C. -6 O d. 4 Oe. 0 Question 6 Use synthetic division to find f(3). Not yet answered Select one: Points out of O a. -10 11.11 O b. 10 O c. O O d. - 12 O e. 12Question 7 Use the Intermediate Value theorem to determine if the statement below is true or false. Not yet answered There is a zero between x = 2 and x = 3. Points out of 11.11 Select one: O True O False Question 8 Use synthetic division to find f N/ OT Not yet answered Points out of Select one: 11.11 O a. 20 Ob. o O c. -20 O d. 10 O e. -10Question 9 Find all zeros of f(x). Not yet answered Select one: Points out of 11.11 O a. {- 1, 2 , 5 O b. - 2, 1 , ? O c. 1-1,0 , NOT NOT O d. - 1 , 1 , O e. 1 , 2 , N /OInformation For questions 1 - 5, combine the functions fand g, as indicated. Question 1 Not yet Find f +g for f(x) = - x -4 and g(x) = x+3 x2 + 3x+2 x2 - 4 answered Points out of Select one: 16.66 O a. 2x2+ 2x-5 (x-2)(x-2)(x+1) O b. 2x2 - 2x+9 (x-2)(x+2)(x+1) O C. 2x + 11 (x-2)(x+2) O d. 2x2 -2x+ 11 (x- 2)(x+2)(x+1)Question 2 Find f - g for f(x) = x+5 and g (x) = - 2 Not yet x - 3 answered Points out of Select one: 16.66 O a. x2- x - 10 (x+5)(x-3) O b. x2-5x - 10 (x+5)(x-3) O c. x- 2 x - 3 O d. x2-5x+ 10 (x+5)(x-3) Question 3 Find f+ g for f(x) =8 and g (x) = 4 Not yet x+2 x- 2 answered Points out of Select one: 16.67 O a. 12 (x+2)(x-2) O b. 12x -8 (x+ 2)(x-2) O c. 48 x+2 Od. 6 X EQuestion 4 Find fg for f(x) = 6x- - 11x+4 and g (x) = - 2x2 + 4x Not yet 3x 3x2 + 2x -8 answered Points out of Select one: 16.67 O a. 2(2x-1)(3x -4) 3(3x +4) O b. 2(2x - 1) 3 O c. (2x-1)(3x -4)2 6x O d. 2(2x-1) (x+2) 3(x - 2) Question 5 Find - for f ( x ) = 2x2+ 3x - 5 and g ( x ) = 10x2+5x-50 Not yet g 4x2 -4 answered 2x2 + 8x+6 Points out of Select one: 16.67 O a. 5(x-2) 8 ( x+3) O b. x+3 10(x -2) O c. 8(x+ 3) 5(x -2) O d. 5(2x+ 5)2( x-2) 8 ( x + 1) 2 ( x+ 3)Question 6 Not yet What is the domain for - x -5 when f(x) = - and g(x) = *-2 g x2 + 6x+5 X-4 answered Points out of Select one: 16.67 O a. all real numbers O b. all real numbers with x*-5, x*-1, x#2, x#4 O c. all real numbers with x*-5, x#-1, x#4 O d. all real numbers with x*-5, x*-1, x#2, x#4, x#5Information For questions 1 - 6, the graph of a function is given. Select the best description of the function's continuity or discontinuity. Question 1 Not yet answered Points out of 14.29 Select one: O a. The function has jump discontinuity at x = 0. O b. The function has removable discontinuity at x = 0. O c. The function is continuous. O d. The function has infinite discontinuity at x = 0.Question 2 Not yet answered Points out of 14.29 Select one: O a. The function has jump discontinuity at x = 2. O b. The function is continuous. O c. The function has removable discontinuity at x = 0. O d. The function has infinite discontinuity at x = -2.Question 3 Not yet answered Points out of 14.29 -4 Select one: O a. The function has removable discontinuity at x = 0. O b. The function is continuous. O c. The function has jump discontinuity at x = 0.5. O d. The function has infinite discontinuity at x = 1.Question 4 Not yet answered Points out of 14.29 Select one: O a. The function has removable discontinuity at x = 4. O b. The function has jump discontinuity at x = 4. O c. The function is continuous. O d. The function has infinite discontinuity at x = -2. O e. The function has infinite discontinuity at x = 4.Question 5 Not yet answered Points out of 14.28 Select one: O a. The function has jump discontinuity at x = 4. O b. The function is continuous. O c. The function is discontinuous at x = 2. O d. The function has removable discontinuity at x = 0.Question 6 Not yet answered Points out of 14.28 Select one: O a. The function has infinite discontinuity at x = -3. O b. The function has jump discontinuity at x = 0.3.