Part A
Complete exercises 86, 88, 90, 92, 94,112, 114, 116, and 118 on page 15 (Section P.1 – Algebraic Expressions and Real Numbers) of the textbook; complete exercises 10, 12, 14, 16, 18, 20, and 22 on page 49 (P.4 - Polynomials); complete exercises 74, 76, 78, 80, and 82 on page 50 (Section P.4).
Section P.1 – Algebraic Expressions and Real Numbers Page 15
Simplify each algebraic expression
86. 2(5x+4)-3
88. 2(5x-1)+14x
90.4(2y-6)+3(5y+10)
92. 4(5y-3)-(6y+3)
94. 6-5[8-(2y-4)]
Write each English phrase as an algebraic expression. Then simplify the expression let x represent the n umber.
112. A number decreased by the difference between eight and the number
114. Ten times the product of negative four and a number
116. the difference between the product of six and a number and negative twice the number
118. Eight decreased by three times the sum of a number and six
Section P.4 - Polynomials Page 49
Perform the indicated operations. Write the resulting polynomial in standard form and indicate it degree.
10. (-7x^(3)+6x^(2)-11x+13)+(19x^(3)-11x^(2)+7x-17)
12. (18x^(4)-2x^(3)-7x+8)-(9x^(4)-6x^(3)-5x+7)
14. (8x^(2)+7x-5)-(3x^(2)-4x)-(-6x^(3)-5x^(2)+3)
16. (x+5)(x^(2)-5x+25)
18. (2x-1)(x^(2)-4x+3)
20. (x+8)(x+5)
22.(x-1)(x+2)
Section P.4 - Polynomials Page 50
Find each product
74. (x+y+5)(x+y-5)
76.(5x+7y-2)(5x+7y+2)
78. [8y+(7-3x)][8y-7(7-3x)]
80. (x+y+2)^2
82. (5x+1+6y)^2
Part B
Complete exercises 12, 14, 16, 20, 22, 24, 26, 28, 66, 68, 70, 72, and 74 on page 60 (P.5 – Factoring Polynomials); complete exercises 2, 4, 6, 16, 18, 20, 38, 40, 42, 52, and 54 on page 74 (P.6 – Rational Expressions).
Section P.5 – Factoring Polynomials Page 60
Factor by grouping
12. x^3-3x^2+4x-12
14. x^3+6x^2-2x-12
16. x^3-x^2-5x+5
Factor each trinomial, or state that the trinomial is prime.
20. x^2-4x-5
22. x^2-14x+45
24. 2x^2+5x-3
26. 3x^2-2x-5
28. 6x^2-17x+12
Factor completely, or state that the polynomial is prime.
66. 5x^3-45x
68. 6x^2-18x-60
70. 7x^4-7
72.x^3+3x^2-25x-75
74. 6x^2-6x-12
P.6 – Rational Expressions Page 74
Find all numbers that must be excluded from the domain of each rational expression.
2.13/x+9
4. x+7/x^2-49
6. x-3/x^2+4x-45
Multiply or dived as indicated.
16. 6x+9/3x-15 * x-5/4x+6
18. x^2-4/x^2-4x+4 * 2x-4/x+2
20. x^2+5x+6/x^2+x-6 * x^2-9/x^2-x-6
Add or subtract as indicated
38. 2x+3/3x-6 – 3-x/3x-6
40. x^2-4x/x^2-x-6 – x-6/x^2-x-6
42. 8/x-2 + 2/x-3
52.x/x^2-2x-24 – x/x^2-7x+6
54.6x^2+17x-40/x^2+x-20 + 3/3-4 – 5x/x+5
Part C
Complete exercises 30, 32, and 34 on page 284 (2.2 – Quadratic Functions); graph the functions defined in exercises 42, 44, 46, and 48 on page 298 (2.3 – Polynomial Functions and Their Graphs); complete exercises 62, 64, 70, 76, and 78 on page 343 (2.6 – Rational Functions and Their Graphs).
2.2 – Quadratic Functions Page 284
Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola’s axis of symmetry. Use the graph to determine the function’s domain and range.
30. f(x)=2x^2-7x-4
32. f(x)=5-4x-x^2
34. f(x)=x^2+4x-1
2.3 – Polynomial Functions and Their Graphs Page 298
a. Use the Leading Coefficient Test to determine the graph’s end behavior.
b. Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.
c. Find the y-intercept.
d. Determine whether the graph has y-axis symmetry, origin symmetry, or neither.
e. If necessary, find a few additional points and graph the function. Use the maximum number of turning points to check whether it is drawn correctly.
42. f(x)=x^3+x^2-4x-4
44. f(x)=x^4-x^2
46. f(x)=-x^4-6x^3+9x^2
2.6 – Rational Functions and Their Graphs Page 343
Strategy for graphing a rational function
1. Determine whether the graph of f has symmetry.
2. Find the y-intercept (if there is one) by evaluating f (0).
3. Find the x-intercepts (if there are any) by solving the equation p(x)=0.
4. Find any vertical asymptote(s) by solving the equation q(x)=0
5. Find the horizontal asymptote (if there is one) using the rule for determining the horizontal asymptote of a rational function.
6. Plot at least one point between and beyond each x-intercept and vertical asymptote.
7. Use the information obtained previously to graph the function between and beyond the vertical asymptotes.
Follow the seven steps to graph each rational function
62. f(x)=4x^2/x^2+1
64. f(x)=x-4/x^2-x-6
70.f(x)=x^2=4x+3/(x+1)^2
a. Find the slant asymptote of the graph of each rational function and
b. Follow the seven-step strategy and use the slant asymptote to graph each rational function.
76. f(x)=x^2=x+1/x-1
78. f(x)=x^3-1/x^2-9