Practice Test 4

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Divide using synthetic division.

1) x4 + 3x3 + x2 + 7x + 5x + 1

1)

A) x3 + 2x2 + x + 6 +6

x + 1 B) x3 + 2x2 - x + 8 -3

x + 1

C) x3 + 2x2 + x + 8 +6

x + 1 D) x3 - 2x2 - x + 6 -3

x + 1

Answer: B

2) x5 + x2 - 4x + 3

2)

A) x4 - 3x3 + 10x2 - 30x + 90 +-274x + 3 B) x4 - 3x3 + 9x2 - 26x + 78 +

-238x + 3

C) x4 - 2x2 +2

x + 3 D) x4 - 2 +2

x + 3

Answer: B

Use synthetic division and the Remainder Theorem to find the indicated function value.3) f(x) = x4 - 4x3 - 6x2 + 4x + 4; f(3) 3)

A) -65 B) 65 C) -195 D) -146Answer: A

4) f(x) = 2x3 - 5x2 - 4x + 7; f(-2) 4)A) -37 B) -21 C) -11 D) -6

Answer: B

Use the Rational Zero Theorem to list all possible rational zeros for the given function.5) f(x) = x5 - 6x2 + 3x + 21 5)

A) ± 1, ± 17

, ± 13

, ± 121 B) ± 1, ± 1

7, ± 1

3, ± 1

21, ± 7, ± 3, ± 21

C) ± 1, ± 7, ± 3 D) ± 1, ± 7, ± 3, ± 21

Answer: D

6) f(x) = -2x3 + 3x2 - 2x + 8 6)

A) ± 12

, ± 1, ± 2, ± 4, ± 8 B) ± 12

, ± 1, ± 2, ± 4

C) ± 14

, ± 12

, ± 1, ± 2, ± 4, ± 8 D) ± 18

, ± 14

, ± 12

, ± 1, ± 2, ± 4, ± 8

Answer: A

1

Find a rational zero of the polynomial function and use it to find all the zeros of the function.7) f(x) = x3 + 2x2 - 9x - 18 7)

A) {-3, -2, 3} B) {-3} C) {-3, 2, 3} D) {-2}Answer: A

8) f(x) = x3 + 3x2 + 4x - 8 8)A) {1, -2 + 2i, -2 - 2i} B) {1, 2 + 2i, 2 - 2i}C) {1, 2 + 3, 2 - 3} D) {-1, -2 + 3, -4 - 3}

Answer: A

Find an nth degree polynomial function with real coefficients satisfying the given conditions.9) n = 3; 3 and i are zeros; f(2) = 10 9)

A) f(x) = 2x3 - 6x2 - 2x + 6 B) f(x) = -2x3 + 6x2 + 2x - 6C) f(x) = -2x3 + 6x2 - 2x + 6 D) f(x) = 2x3 - 6x2 + 2x - 6

Answer: C

10) n = 3; - 6 and i are zeros; f(-3) = 60 10)A) f(x) = 2x3 + 12x2 - 2x - 12 B) f(x) = 2x3 + 12x2 + 2x + 12C) f(x) = -2x3 - 12x2 - 2x - 12 D) f(x) = -2x3 - 12x2 + 2x + 12

Answer: B

11) n = 4; 2i, 5, and -5 are zeros; leading coefficient is 1 11)A) f(x) = x4 + 4x2 - 100 B) f(x) = x4 + 4x3 - 21x2 - 100C) f(x) = x4 - 21x2 - 100 D) f(x) = x4 + 4x2 - 5x - 100

Answer: C

Solve the problem.12) Solve the equation 2x3 - 23x2 + 71x - 30 = 0 given that 5 is a zero of f(x) = 2x3 - 23x2 + 71x - 30. 12)

A) 5, 1, 3 B) 5, -6, -12 C) 5, 6, 1

2 D) 5, -1, - 3

Answer: C

Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solvethe polynomial equation.

13) 5x3 - 18x2 - 11x + 12 = 0; -1 13)

A) 45

, 3, -1 B) 35

, -4, -1 C) -35

, 4, -1 D) 35

, 4, -1

Answer: D

Write the equation in its equivalent exponential form.14) log 5 25 = 2 14)

A) 525 = 2 B) 52 = 25 C) 25 = 25 D) 252 = 5Answer: B

15) log 6 36 = x 15)

A) 36x = 6 B) 366 = x C) 6x = 36 D) x6 = 36Answer: C

2

Write the equation in its equivalent logarithmic form.

16) 5-2 =125 16)

A) log 1/5 5 = -2 B) log-2

125

= 5 C) log 5125

= -2 D) log 5 -2 =125

Answer: C

17)3

64 = 4 17)

A) log 64 3 =14 B) log 64 4 =

13 C) log 4 64 = 3 D) log 4 64 =

13

Answer: B

18) 72 = 49 18)A) log 7 2 = 49 B) log 49 7 = 2 C) log 2 49 = 7 D) log 7 49 = 2

Answer: D

Evaluate the expression without using a calculator.19) log 4 16 19)

A) 8 B) 1 C) 12 D) 2

Answer: D

20) log 3 3 20)

A) 3 B) 13 C) 1

2 D) 1

Answer: C

21) log 4116 21)

A) 2 B) -2 C) 8 D) 12

Answer: B

22) log717

22)

A) 17 B) -

17 C) 1

2 D) -12

Answer: D

23) log 5 1 23)

A) 1 B) 5 C) 15 D) 0

Answer: D

3

24) log 5 5 24)

A) 0 B) 5 C) 1 D) 15

Answer: C

Evaluate or simplify the expression without using a calculator.25) log 10,000 25)

A) 40 B) 4 C) 25 D) 1

4

Answer: B

Evaluate the expression without using a calculator.26) log 3 314 26)

A) 14 B) 3 C) log 3 14 D) 17

Answer: A

Evaluate or simplify the expression without using a calculator.

27) log 110,000 27)

A) 4 B) -4 C) 110,000 D) -

14

Answer: B

28) log 0.01 28)

A) -2 B) -12 C) 1

2 D) 2

Answer: A

29) 8 log 104.1 29)A) 328 B) 3.28 C) 11.2879 D) 32.8

Answer: D

30) 10log 4 30)A) 40 B) 0.0001 C) 10,000 D) 4

Answer: D

31) ln7

e 31)

A) 7e B) e7 C) 1

7 D) 7

Answer: C

32) ln e3 32)

A) 3 B) 1 C) e D) 13

Answer: A

4

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluatelogarithmic expressions without using a calculator.

33) log 7 (7x) 33)A) x B) 7 C) 1 + log 7 x D) 1

Answer: C

34) log x100 34)

A) log x + 2 B) 100x C) -20x D) log x - 2Answer: D

35) log 4x + 3x4 35)

A) log 4 (x + 3) - 4 log 4 x B) log 4 (x + 3) + 4 log 4 xC) log 4 (x + 3) - log 4 x D) 4 log 4 x - log 4 (x + 3)

Answer: A

36) logbxy2

z5 36)

A) logbx + 2logby - 5logbz B) logbx + logby2 + logbz5

C) logbx + 2logby + 5logbz D) logbx + logby2 - logbz5

Answer: A

37) log 3x3 33 - x

4(x + 3)237)

A) log 3 + 3log x +13

log (3 - x) - log 4 - 2log (x + 3)

B) log 3 + 3log x +13

log (3 - x) - log 4 + 2log (x + 3)

C) log 3 + log x3 + log (3 - x)1/3 - log 4 - log (x + 3)2

D) log (3x3 33 - x) - log (4(x + 3)2)

Answer: A

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whosecoefficient is 1. Where possible, evaluate logarithmic expressions.

38) 6 ln x -14

ln y 38)

A) ln x64

yB) ln x6y4 C) ln x6 4

y D) ln x6

y4

Answer: A

5

39) 13

[2ln (x + 8) - ln x - ln (x2 - 9)] 39)

A) ln 3 2(x + 8)x(x2 - 9)

B) ln 3 (x + 8)2

x(x2 - 9)

C) ln 3 (x + 8)2(x2 - 9)x

D) ln 3 x(x + 8)2

(x2 - 9)

Answer: B

40) log x + log (x2 - 121) - log 9 - log (x - 11) 40)

A) log x(x - 121)(x - 11)9 B) log 2x + 11)

20 - x

C) log x(x + 11)9 D) log x(x - 121)

9(x - 11)

Answer: C

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places41) log 24 386 41)

A) 0.5336 B) 3.9668 C) 1.8741 D) 1.2064Answer: C

42) log 16 42)A) 0.7070 B) 1.7013 C) 2.4220 D) 0.4129

Answer: C

Solve the equation by expressing each side as a power of the same base and then equating exponents.43) 4(1 + 2x) = 64 43)

A) {4} B) {1} C) {-1} D) {16}Answer: B

44) 125x =15

44)

A) 16 B) -

13 C) -

16 D) {-3}

Answer: C

45) 32x = 8 45)

A) 53 B) 3

4 C) 35 D) {3}

Answer: C

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for thesolution.

46) 3 x + 6 = 8 46)A) 1.31 B) -0.35 C) 6.53 D) -4.11

Answer: D

6

47) e x + 2 = 5 47)A) -0.30 B) 1.95 C) -0.39 D) -0.05

Answer: C

48) e2x + ex - 6 = 0 48)A) 0.69, 1.10 B) 1.10, 0.14 C) 0.14 D) 0.69

Answer: D

Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmicexpressions. Give the exact answer.

49) log 5 (x - 1) = 3 49)A) {126} B) {242} C) {244} D) {124}

Answer: A

50) log2

x + log2

(x - 3) = 2 50)

A) {2} B) {1, -4} C) {4} D) {-1, 4}Answer: C

51) log4

(x + 2) - log4

x = 2 51)

A) {18

} B) {152

} C) {4} D) { 215

}

Answer: D

52) log x + log (x -1) = log 30 52)

A) {-5} B) {6, -5} C) 312 D) {6}

Answer: D

53) log (x + 23) - log 3 = log (10x + 3) 53)

A) 1429 B) -

667 C) -

1429 D) 66

7

Answer: A

Graph the function by making a table of coordinates.54) f(x) = 4x 54)

7

A) B)

C) D)

Answer: A

55) f(x) =14

x55)

8

A) B)

C) D)

Answer: C

Graph the function.56) Use the graph of f(x) = ex to obtain the graph of g(x) = ex + 4. 56)

9

A) B)

C) D)

Answer: D

57) Use the graph of log 3 x to obtain the graph of f(x) = log 3 (x - 1). 57)

10

A) B)

C) D)

Answer: B

58) Use the graph of log 5 x to obtain the graph of f(x) = -2 + log 5 x. 58)

11

A) B)

C) D)

Answer: C

12