Free Printable Ch 7 Review

1.

Evaluate $5x^4\cdot4x^5$

a)

$\frac{4}{x^2}$

b)

4

c)

$20x^9$

d)

$\frac{9}{x^4}$

2.

Evaluate $3v^2\cdot5v^{-3}$

a)

$\frac{15}{v}$

b)

$20v$

c)

$20v^5$

d)

$15v^5$

3.

Evaluate $5n^{-4}\cdot2n^6$

a)

$\frac{18}{n}$

b)

$\frac{12}{n^9}$

c)

$18n^7$

d)

$10n^2$

4.

Evaluate $x^3\cdot2x^{-6}$

a)

$24x^3$

b)

$\frac{2}{x^3}$

c)

$\frac{15}{x^3}$

d)

$6x^3$

5.

Simplify $\frac{5r^6}{4r^3}$

a)

$\frac{3}{r^2}$

b)

$\frac{3r}{2}$

c)

$\frac{5r^4}{4}$

d)

$\frac{5r^3}{4}$

6.

Simplify $\frac{6x^{-5}}{5x^6}$

a)

$\frac{3}{2x^4}$

b)

$\frac{6}{5x^{11}}$

c)

$\frac{1}{2x^3}$

d)

$\frac{6x^2}{5}$

7.

Simplify $\frac{5x^3}{2x^{-6}}$

a)

$\frac{3x^4}{2}$

b)

$x^9$

c)

$\frac{5x^9}{2}$

d)

$\frac{1}{3x^2}$

8.

Evaluate $\frac{6n^2}{6n^{-2}}$

a)

$n^4$

b)

$\frac{1}{3n^{10}}$

c)

$\frac{4}{3n^4}$

d)

$4n^3$

9.

Simplify $\left(5x^3\right)^2$

a)

$8x^{15}$

b)

$25x^6$

c)

$9x^4$

d)

$\frac{1}{3125x^5}$

10.

Simplify $\left(p^3\right)^6$

a)

$\frac{1}{243p^{25}}$

b)

$125p^{18}$

c)

$\frac{1}{p^8}$

d)

$p^{18}$

11.

Simplify $\left(2p^3\right)^{-3}$

a)

$16p^{10}$

b)

$\frac{1}{8p^9}$

c)

$\frac{8}{p^9}$

d)

$243p^{10}$

12.

$\left(2n^{-3}\right)^5$

a)

$\frac{36}{n^{10}}$

b)

$\frac{1}{n^4}$

c)

$\frac{32}{n^{15}}$

d)

$256n^8$

13.

Solve 5^-2

a)

-10

b)

1/25

c)

1/(5)²

d)

-1/10

14.

What is 10⁰equivalent to?

a)

1

b)

10

c)

0

d)

100

15.

Simplify (34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

16.

Simplify -5p⁰t^-5/ 2^-1m²

a)

-5p/2t⁵m²

b)

10m²/t⁵

c)

(-5)(2)/t⁵m²

d)

-10/t⁵m²

17.

Write with positive exponents:

a)

a^-2

b)

a²

c)

1/a¹

18.

Simplify x²y^-5

a)

x²/y⁵

b)

1/x²y⁵

c)

y⁵/x²

d)

x²/y^-5

19.

(c⁵)(c³)(c³)

a)

c⁴⁵

b)

3c¹¹

c)

c¹¹

d)

3c⁴⁵

20.

t⁶³•t

a)

t⁶⁴

b)

t⁶³

21.

(x¹⁴)³

a)

x¹⁷

b)

x⁴²

c)

x¹¹

d)

3x¹⁴

22.

(6x²)(-3x⁵)

a)

18x⁷

b)

-18x⁷

c)

18x⁷

d)

3x⁷

23.

CHALLENGE:
3x³y * 2x⁸y⁵

a)

5x¹¹y⁶

b)

6x¹¹y⁶

c)

6x²⁴y⁵

d)

3x¹¹2y⁵

24.

18h¹⁰÷ 6h⁸

a)

3h¹⁸

b)

3h⁸⁰

c)

2h²

d)

3h²

25.

12h⁸÷ 3h⁴

a)

4h¹²

b)

9h⁴

c)

4h⁴

d)

9h¹²

26.

Simplify

a)

x²⁸y¹² / x²y

b)

x²⁸y¹² / x⁸y⁴

c)

x²⁰y⁸

27.

Simplify the following:
(3ab²)³

a)

27a³b⁶

b)

3ab⁶

c)

3a³b⁶

d)

27ab²

28.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

29.

Solve (hint: there's more than 1 law you must obey)

a)

x²⁸y¹² / x²y

b)

x²⁸y¹² / x⁸y⁴

c)

x²⁰y⁸

30.

1⁄4x⁻⁵

a)

x⁵⁄4

b)

4x⁵

c)

-4x⁵

d)

-x⁵⁄4

31.

a)

A

b)

B

c)

C

d)

D

32.

a)

A

b)

B

c)

C

d)

D

33.

Use either long division or synthetic division

a)

x - 7

b)

x²- 7

c)

x + 7

d)

x²+ 3x - 54

34.

Use either long division or synthetic division

a)

2x³ + 3x + (7/x-4)

b)

2x² + 3x + 8 + (7/x-4)

c)

2x² + 3x + 8

d)

2x² - x + 10 + (6/x-4)

35.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

36.

Divide using synthetic division
(2x³ + 4x² - 5) by (x + 3).

a)

2x² + 2x - 4 R(-12)

b)

2x² - 2x + 6 R(-23)

c)

2x² - 2x + 8 R(-20)

d)

2x² - 4x + 1 R0

37.

a)

x + 5 + (2/2x - 4)

b)

x - 8

c)

x - 5 + (3/2x - 4)

d)

x + 5

38.

The answer to a division problem is known as the...?

a)

product

b)

sum

c)

difference

d)

quotient

39.

What does it mean to be a factor of a number?

a)

Divides evenly with a remainder of zero.

b)

Divides unevenly with a remainder of 1.

40.

If you are missing a term in your polynomials (both dividend and divisor), you must put a zero as a coefficient place holder for that term.

a)

True

b)

False

c)

Only for the dividend

d)

Only for the divisor

41.

If 𝒙²+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?

a)

0

b)

-3

c)

9

d)

5

42.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

43.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

44.

What is the quotient when (10n²- 37n - 12) is divided by (n - 4)?

a)

(10n - 3)

b)

(3n - 10)

c)

(10n + 3)

d)

(3n + 10)

45.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

46.

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/x-2

d)

2x² - 9x - 15 - 23/x-2

47.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

48.

(3x³ - 2x² - 7x + 6) ÷ (x + 1)

a)

3x³ - 5x² - 2x + 8

b)

3x² + x - 6

c)

3x² - 5x - 2 + 8/x+1

d)

3x³ + x² - 6x

49.

(2x³ + 7x² - 6x - 8) ÷ (x + 4)

a)

2x² - x - 2

b)

2x³ - x² - 2x

c)

2x² + 15x + 54 + 208/x+4

d)

2x³ + 15x² + 54x + 208

50.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

51.

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

a)

Cam wrote the remainder incorrectly.

b)

Cam did not use a zero place holder for the x³ term.

c)

Cam added instead of subtracting the rows.

d)

Cam should have used -2 as his division since the factor was x-2.

52.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

53.

a)

x - 7

b)

x²- 7

c)

x + 7

d)

x²+ 3x - 54

54.

What is the remainder of (4x³ - 3x² - 4x +2) ÷ (x - 3)?

a)

-71

b)

71

c)

145

55.

What is the remainder of (x³ - 5x² - 8x +1) ÷ (x + 1)?

a)

-13

b)

1

c)

3

56.

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x³- 5x²+ 2x - 10

a)

0

b)

2x-10

c)

-2x-10

d)

2x+10

57.

a)

A

b)

B

c)

C

d)

D

58.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x-12

b)

2x⁴-x³-25x²-12x+0

59.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x-12

b)

2x⁴-x³-25x²-12x+0

60.

Divide using synthetic division
(2x³ + 4x² - 5) by (x + 3).

a)

2x² + 2x - 4 R(-12)

b)

2x² - 2x + 6 R(-23)

c)

2x² - 2x + 8 R(-20)

d)

2x² - 4x + 1 R0

61.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

62.

(3x³ + 5x - 1) ÷ (x + 1)

a)

3x³ - 3x² + 8x - 9

b)

3x² - 3x + 8 - 9/x+1

c)

3x² + 3x + 8 + 7/x+1

d)

3x³ + 3x² + 8x + 7

63.

(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

64.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

65.

If you are missing an exponent in your polynomial you must put a zero as a coefficient place holder for that exponent

a)

True

b)

False

66.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

67.

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

a)

Cam wrote the remainder incorrectly.

b)

Cam did not use a zero place holder for the x³ term.

c)

Cam added instead of subtracting the rows.

d)

Cam should have used -2 as his division since the factor was x-2.

68.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

69.

a)

x - 7

b)

x²- 7

c)

x + 7

d)

x²+ 3x - 54

70.

a)

2x³ + 3x + (7/x-4)

b)

2x² + 3x + 8 + (7/x-4)

c)

2x² + 3x + 8

d)

2x² - x + 10 + (6/x-4)

71.

Divide using synthetic division
(2x³ + 4x² - 5) by (x + 3).

a)

2x² + 2x - 4 R(-12)

b)

2x² - 2x + 6 R(-23)

c)

2x² - 2x + 8 R(-20)

d)

2x² - 4x + 1 R0

72.

a)

x + 5 + (2/2x - 4)

b)

x - 8

c)

x - 5 + (3/2x - 4)

d)

x + 5

73.

If 𝒙²+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?

a)

0

b)

-3

c)

9

d)

5

74.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

75.

What is the quotient when (10n²- 37n - 12) is divided by (n - 4)?

a)

(10n - 3)

b)

(3n - 10)

c)

(10n + 3)

d)

(3n + 10)

76.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

77.

Divide using long division:
(4x² - 24x + 35) ÷ (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

78.

Divide using Synthetic Division
(3x² + 6) ÷ (x + 2)

a)

-3x

b)

0

c)

3x

d)

-0

79.

Divide using long division
(4b² + b - 2) ÷ (4b + 5)

a)

b + 1 - 3/4b +5

b)

b - 1 + 3/4b - 5

c)

b + 1 + 3/4b + 5

d)

b - 1 + 3/4b + 5

80.

Divide using synthetic division
(5x² - 16x - 16) ÷ (x-4)

a)

(5x - 4)

b)

(5x + 4)

c)

(-5x - 4)

d)

(-5x + 4)

81.

Divide using synthetic divistion
(5n² + 17n - 15) ÷ (n + 4)

a)

-5n - 3 - 3/n + 4

b)

5n + 3 + 3/n - 4

c)

5n - 3 - 3/n + 4

d)

_5n + 3 + 3/n - 4

82.

Factor

x³ + 3x² - 5x - 15

a)

(x²+5)(x+3)

b)

(x²+5)(x-3)

c)

(x²-5)(x-3)

d)

(x²-5)(x+3)

83.

Factor

3n³ + 4n² - 18n - 24

a)

(4n²-3)(n+6)

b)

(n²+6)(3n+4)

c)

(n²-6)(3n+4)

d)

(4n²+3)(n-6)

84.

Factor

r³ - 4r² + 6r - 24

a)

(r²+6)(r-4)

b)

(r²-4)(r+6)

c)

(r²-6)(r-4)

d)

(2r²+2)(r-6)

85.

Factor

27x³ - 64y³

a)

(4x-3y)³

b)

(3x-4y)³

c)

(9x-21.3y)³

d)

(3x+4y)³

86.

Factor

a⁶ x³ + b⁹ y⁶

a)

(a²x + b³y²) (a⁴x² - a²xb³y² + b⁶y⁴)

b)

(a²x + b³y²) (a⁴x² - a²xb³y² - b⁶y⁴)

c)

(a²x + b³y²) (a⁴x² + a²xb³y² + b⁶y⁴)

d)

(a²x + b³y²) (a⁴x² + a²xb³y² - b⁶y⁴)

87.

Factor

8 - 125t³

a)

(5-2t)(25t²+10t+4)

b)

(2-5t)(25t²-10t-4)

c)

(5+2t)(25t²+10t+4)

d)

(2-5t)(25t²+10t+4)

88.

Factor

x³ - 3x² - 10x

a)

x(x²+3x-10)

b)

x(x²-3x+10)

c)

x(x+5)(x+2)

d)

x(x-5)(x+2)

89.

Factor

2x³ - 9x² + 4x

a)

x(2x+1)(x-4)

b)

x(2x-1)(x+4)

c)

x(4x+1)(x+2)

d)

x(2x-1)(x-4)

90.

Factor

x³ +5x²

a)

(x²+1)(x+5)

b)

x(x²+5)

c)

x²(x-5)

d)

x²(x+5)

91.

Factor

r³ + 3r²s + 3rs² + s³

a)

(r²-3rs²)(s+3r²s)

b)

(r+s)³

c)

(r-s)³

d)

(r²+3r²s)(s+3rs²)

92.

Factor by Grouping: $2x^3+14x^2+5x+35$

93.

Factor by Grouping: $x^3+3x^2+4x+12$

94.

Factor by Grouping: $x^3+5x^2-2x-10$

95.

Factor by Grouping: $x^3+3x^2+2x+6$

96.

Factor by Grouping:

p⁴- 3p³ - 16p² + 48p

a)

p² ( p - 3) (p - 3)

b)

(p³ - 16) (p - 3)

c)

(p + 4) (p - 4) (p - 3)

d)

(p³ - 16p) (p - 3)

97.

Factor by Grouping:

4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

98.

Factor by Grouping:

3x³-x²+6x-2

a)

(x²+2)(3x+1)

b)

(x²+2)(3x-1)

c)

(3x³+6x)(x²-2)

d)

none of the above

99.

Factor

k⁴+7k²+10

a)

(k²+2)(k²+5)

b)

(k²-2)(k²-5)

c)

(k+10)(k+4)

d)

(k+2)(k+5)

100.

Factor

2x⁴ - 13x² - 70

a)

(2x+7)(x-10)

b)

(7x+5)(x+2)

c)

(2x²+7)(x²-10)

d)

2(x²+7)(x²+10)

101.

Factor Completely: 3x²+15x-72

a)

x(x+5)

b)

3(x+8)(x-3)

c)

(3x+24)(x-3)

d)

3(x-8)(x+3)

102.

Factor Completely: x⁴-9x²

a)

x²(x+3)(x-3)

b)

(x²+3x)(x²-3x)

c)

(x²+9)(x-3)(x+3)

d)

x²(x²-9)

103.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

104.

Factor
81m² - 1

a)

not factorable

b)

(m-9)(m+9)

c)

9m(9m-1)

d)

(9m-1)(9m+1)

105.

Factor:
2x² - 3x - 2

a)

(2x - 2)(x + 1)

b)

(2x + 1)(x - 2)

c)

(2x - 1)(x - 2)

d)

(2x - 1) (x - 1)

106.

What is the width of this rectangle?

a)

5x⁴ + 10x³

b)

x + 15x³

c)

x + 3

d)

x⁴ + 3x³

107.

A rectangle has an area of 4x²+19x + 12 and a length of (x + 4). What is the width?

a)

4x - 3

b)

4x + 3

c)

2x + 6

d)

2x + 3

108.

a)

A

b)

B

c)

C

d)

D

109.

Factor the GCF
39y⁵ + 12y⁴- 3y³

a)

3y(13y⁴ + 4y³ - y²)

b)

3y³(13y² + 4y - 1)

c)

y³(39y² + 12y - 3)

d)

not factorable

110.

Factor the GCF
4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

111.

Factor by grouping

x³ - 4x² - 4x + 16

a)

(x+4)(x+2)

b)

(x-4)(x² -4)

c)

(x+4)(x² -4)

d)

(x-4)(x-2)

112.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

113.

Factor by grouping:
5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

114.

Factor by grouping:

2x³-8x²-x+4

a)

(2x²-1)(x-4)

b)

2(x²-1)(x+4)

c)

(x²-1)(2x-4)

d)

(2x²+1)(x-4)

115.

Factor by grouping:

20x³-25x²+4x-5

a)

(5x²-5)(4x+1)

b)

5(x²-1)(4x+5)

c)

(5x²+1)(4x-5)

d)

(5x²+1)(4x-1)

116.

Factor by grouping:

7r³-8r²+42r-48

a)

(r²+6)(7r+8)

b)

(r²+6)(7r-8)

c)

(r²+6)(r²+8)

d)

(r²+6)(7r+6)

117.

Solve

a² - 9 = 0

a)

a = -1, 9

b)

a = 1, -9

c)

a = 3, -3

d)

a = 0, 9

118.

Solve by factoring: $5x^2-45=0$

a)

$x=3$

b)

$x=-3$

c)

$x=3$ and $x=-3$

d)

$x=0$ , $x=3$ , and $x=-3$

119.

Solve by factoring: $2x^2-x-15=0$

a)

$x=-\frac{5}{2}$ and $x=3$

b)

$x=\frac{5}{2}$ and $x=-3$

c)

$x=\frac{5}{2}$ and $x=3$

d)

$x=-\frac{5}{2}$ and $x=-3$

120.

Solve by factoring: 3x³ + 15x² + 30x = 0

a)

3, -3, -2

b)

0, -2, -3

c)

0, 2, 3

d)

0, -6, 1

121.

Solve by factoring: $4x^2+15x+14=0$

a)

$x=\frac{7}{4}$ and $x=2$

b)

$x=-\frac{7}{4}$ and $x=2$

c)

$x=\frac{7}{4}$ and $x=-2$

d)

$x=-\frac{7}{4}$ and $x=-2$

122.

Solve by factoring:

x³+ 3x²- 4x -12 = 0

a)

4, -3

b)

2, 3, -2

c)

2, -3

d)

-2, -3, 2

123.

Solve by factoring x³ + 9x² + 18x = 0

a)

0, -6, -3

b)

0, -9, 2

c)

0 6, 3

d)

-6, -3

124.

Challenge problem: Find the solutions (select all that apply)

3y^3=-21y

a)

$y=\pm7$

b)

$y=0$

c)

$y=\pm7i$

d)

$y=\pm i\sqrt{7}$

125.

Find the zeros: (select all that apply)

f\left(x\right)=5w^3-125w

a)

$w=5$

b)

$w=-5$

c)

$w=0$

d)

$w=25$

e)

$w=5i$

126.

Find the zeros. $g\left(x\right)=3x^3-15x^2-72x$

(select all that apply)

a)

$x=-3$

b)

$x=8$

c)

$x=-7$

d)

$x=0$

e)

$x=3$

127.

Solve the following polynomial. $x^4+16=8x^2$

(select all that apply)

a)

$x=0$

b)

$x=\pm2$

c)

$x=\pm4$

d)

$x=8$

e)

$x=1$

128.

Solve the following polynomial. $0=x^3-3x^2-4x+12$

(select all that apply)

a)

$x=\pm2$

b)

$x=3$

c)

$x=1$

d)

$x=0$

129.

Solve: $4x^4+15x^2-4=0$

a)

$x=\pm\frac{1}{2},\ \pm2i$

b)

$x=\pm\frac{1}{4},\ \pm2$

c)

$x=\pm\frac{1}{2},\ \pm i\sqrt{2}$

d)

$x=\pm4$

130.

Solve: $x^5=16x$

a)

$x=0,\ \pm2,\ \pm2i$

b)

$x=\pm2,\ \pm4i$

c)

$x=0,\ \pm2$

d)

$x=\pm2i,\ \pm4$

131.

Solve: $x^2+4x=45$

a)

$x=-9,\ 5$

b)

$x=9,\ 5$

c)

$x=-9,\ -5$

d)

$x=9,\ -5$

132.

Solve: $2x^4-5x^2-3=0$

a)

$x=\pm\frac{1}{2},\ \pm\sqrt{3}$

b)

$x=\pm\frac{1}{2}i,\pm i\sqrt{3}$

c)

$x=\pm\frac{\sqrt{2}}{2}i,\ \pm\sqrt{3}$

d)

$x=\pm\frac{\sqrt{2}}{2},\ \pm i\sqrt{3}$

133.

Solve: $x^4-12x^3+32x^2=0$

a)

$x=0,\ \pm4$

b)

$x=0,\ -8,\ -4$

c)

$x=0,\ 4,\ 8$

d)

$x=0,\ -16,\ 2$

134.

Solve: $x^4-x^3+x^2-x=0$

a)

$x=0,\ \pm1$

b)

$x=0,\ \pm2,\ 1$

c)

$x=0,\ 1,\ \pm i$

d)

$x=\pm1,\ \pm i$

135.

Solve: $4x^3-3x^2+16x-12=0$

a)

$x=\pm2,\ \frac{3}{4}$

b)

$x=\pm2i,\ \frac{3}{4}$

c)

$x=\pm4,\ \frac{4}{3}$

d)

$x=\pm i\sqrt{2},\ \frac{3}{4}$

136.

Solve: $9x^3-25x=0$

a)

$x=0,\ \pm\frac{5}{3}$

b)

$x=0,\ \pm\frac{3}{5}$

c)

$x=0,\ 3,\ 5$

d)

$x=0,\ -5,\ -3$

137.

Solve: $x^4=x^3+6x^2$

a)

$x=0,\ 3,\ -2$

b)

$x=0,\ -3,\ 2$

c)

$x=0,\ 3$

d)

$x=2,\ -3$

138.

Solve: $5x^3-16x^2+3x=0$

a)

$x=0,\ -\frac{4}{3},\ 1$

b)

$x=0,\ -\frac{1}{5},\ 1$

c)

$x=0,\ \frac{1}{5},\ -\frac{8}{3}$

d)

$x=0,\ \frac{1}{5},\ 3$

139.

Solve: $x^3+3x^2+2x+6=0$

a)

$x=-4,\ \pm1$

b)

$x=-5,\ \pm i\sqrt{2}$

c)

$x=-4,\ \pm i\sqrt{2}$

d)

$x=-3,\ \pm i\sqrt{2}$

140.

Identify the zeros:

a)

x=-2, x=-1, x=0

b)

x=-2, x=0

c)

x=-1, x=0, x=2

d)

x=-2, x=0, x=1

141.

a)

The function has an Even degree

b)

The function has a Negative coefficient

c)

The function has an Odd degree

d)

The function has 3 real zeros

142.

a)

Positive Odd

b)

Positive Even

c)

Negative Odd

d)

Negative Even

143.

What is the end-behavior of the function
y = -x³ + 6x² + 7x

a)

as x-> -∞ f(x) -> ∞
as x-> ∞ f(x) -> -∞

b)

as x-> -∞ f(x) -> ∞
as x-> ∞ f(x) -> ∞

c)

as x->-∞ f(x) -> -∞
as x-> ∞ f(x) -> ∞

d)

as x-> -∞ f(x) -> -∞
as x-> ∞ f(x) -> -∞

144.

What is the end-behavior of the function
y = x⁶ - 7x⁵ + 7x - 9

a)

as x-> -∞ f(x) -> ∞
as x-> ∞ f(x) -> -∞

b)

as x-> -∞ f(x) -> ∞
as x-> ∞ f(x) -> ∞

c)

as x->-∞ f(x) -> -∞
as x-> ∞ f(x) -> ∞

d)

as x-> -∞ f(x) -> -∞
as x-> ∞ f(x) -> -∞

145.

a)

2

b)

1

c)

4

d)

cannot be determined

146.

What is the range of the function behind this text?

a)

ALL, or (-∞,∞)

b)

~ E.B. -5, or (-∞,-5)

c)

~ E.A. -5, or (-5, ∞)

d)

None

147.

a)

The function has an Even degree

b)

The function has a Negative coefficient

c)

The function has an Odd degree

d)

The function has 3 real zeros

148.

What is the range of the function?

a)

(-∞,∞)

b)

(-∞,-5)

c)

(-5, ∞)

d)

[-5, ∞)

149.

Which is true about the equation of the graph shown?

a)

The function has an odd degree

b)

The function has an even degree

c)

The function has 5 real zeros

d)

The function has a positive leading coefficient

150.

What is the remainder when x⁴ - 5 is divided by x + 3?

a)

76

b)

81

c)

7

151.

What is the remainder of (4x³ - 3x² - 4x +2) ÷ (x - 3)?

a)

-71

b)

71

c)

145

152.

What is the remainder of (x³ - 5x² - 8x +1) ÷ (x + 1)?

a)

-13

b)

1

c)

3

153.

If f(x) = 5x² ─ 7x ─10, find the value of f (5) using synthetic division.

a)

150

b)

80

c)

70

154.

What is the remainder when (x¹³ + 10) is divided by (x + 1)?

a)

9

b)

10

c)

11

155.

What is the remainder when (5x²⁰ – 19) is divided by (x ─ 1)?

a)

81

b)

14

c)

- 14

156.

Given P(x) = x³ + x² – x ─ 9, what is the value of P (4)?

a)

14

b)

-53

c)

67

157.

Find the remainder when P(x) = 3x² + 5x + 10 is divided by 3x ─ 1 .

a)

3

b)

6

c)

12

158.

The expression x³ ─ kx² +2x +5 leaves a remainder of 2 when divided by x ─ 3. Find the value of k.

a)

4

b)

-4

c)

8

159.

What is the remainder when n³ - 7 is divided by n + 5 ?

a)

118

b)

132

c)

-132

Ch 7 Review

Total questions: 159

Worksheet time: 13hrs 28mins

Similar Resources on Wayground