Simplify. Write each answer in standard form.

44. ( 5 x 2 − 3 x + 7 x ) + ( 9 x 2 + 2 x 2 + 7 x ) open , 5 x squared , minus 3 x plus 7 x close plus open , 9 x squared , plus , 2 x squared , plus 7 x close
45. ( y 3 − 4 y 2 − 2 ) − ( 6 y 3 + 4 − 6 y 2 ) open , y cubed , minus , 4 y squared , minus 2 close minus open , 6 y cubed , plus 4 minus , 6 y squared , close
46. ( − 9 r 3 + 2 r − 1 ) − ( − 5 r 2 + r + 8 ) open negative , 9 r cubed , plus 2 r minus 1 close minus open negative , 5 r squared , plus r plus 8 close
47. ( 3 z 3 − 4 z + 7 z 2 ) + ( 8 z 2 − 6 z − 5 ) open , 3 z cubed , minus 4 z plus , 7 z squared , close plus open , 8 z squared , minus 6 z minus 5 close
48. Reasoning Is it possible to write a trinomial with degree 0? Explain.
49. Writing Is the sum of two trinomials always a trinomial? Explain.

C Challenge

50. 1. Write the equations for line p and line q. Use slope-intercept form.
    2. Use your equations from part (a) to write a function for the vertical distance D(x) between points on lines p and q with the same x-value.
    3. For what value of x does D(x) equal zero?

    4. Reasoning How does the x-value in part (c) relate to the graph?

       

Simplify each expression.

51. ( a b 2 + b a 3 ) + ( 4 a 3 b − a b 2 − 5 a b ) open eh , b squared , plus b , eh cubed , close plus open , 4 eh cubed , b minus eh , b squared , minus 5 eh b close
52. ( 9 p q 6 − 11 p 4 q ) − ( − 5 p q 6 + p 4 q 4 ) open 9 p , q to the sixth , minus , 11 p to the fourth , q close minus open negative 5 p , q to the sixth , plus , p to the fourth , q to the fourth , close

Standardized Test Prep

SAT/ACT

53. What is a simpler form of ( 3 x 2 + 6 x − 1 ) + ( 4 x 2 + 5 x + 9 ) ? open , 3 x squared , plus 6 x minus 1 close plus open , 4 x squared , plus 5 x plus 9 close question mark

    1. − x 2 + x − 10 negative , x squared , plus x minus 10
    2. − x 2 − x + 10 negative , x squared , minus x plus 10
    3. 7 x 2 + 11 x + 8 7 x squared , plus 11 x plus 8
    4. 7 x 2 + 11 x + 10 7 x squared , plus 11 x plus 10

54. The price of a gift basket of food can be modeled by a linear equation. You can use the graph below to find the price of the basket y, based on pounds of food x. What is the equation of the line?

    

    6. y = 5 x + 10 y equals 5 x plus 10
    7. y = x + 10 y equals x plus 10
    8. y = 10 x + 5 y equals 10 x plus 5
    9. y = 10 x + 10 y equals 10 x plus 10

Short Response

55. Simplify ( 8 x 3 − 5 x + 1 ) − ( x 2 + 4 ) . open , 8 x cubed , minus 5 x plus 1 close minus open , x squared , plus 4 close .  Show your work.

Mixed Review

See Lesson 7-7.

Identify the growth factor in each exponential function.

56. y = 7 · 3 x y equals 7 middle dot , 3 to the x
57. y = 0.3 · 2 . 1 x y equals 0.3 middle dot 2 . , 1 to the x
58. y = 3 · 4 x y equals 3 middle dot , 4 to the x
59. y = 0.2 · 5 x y equals 0.2 middle dot , 5 to the x

See Lesson 5-1.

Find the slope of the line that passes through each pair of points.

60. (0, 2), (5, 0)
61. (3, − 7 negative 7 ), (4, 1)
62. ( − 2 , negative 2 comma  8), (1, 0)
63. ( 9 , − 6 ) , ( 0 , 0 ) open 9 comma negative 6 close comma open 0 comma 0 close

Get Ready! To prepare for Lesson 8-2, do Exercises 64–67.

See Lesson 7-3.

Simplify each expression.

64. a − 3 a 8 eh super negative 3 end super . eh to the eighth
65. 6 r 2 · 3 r 6 r squared , middle dot 3 r
66. ( 4 x 5 ) ( 7 x 3 ) open , 4 x to the fifth , close open , 7 x cubed , close
67. ( 2 t 4 ) ( − 5 t 2 ) open , 2 t to the fourth , close open negative , 5 t squared , close

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