Free Printable A2-CHAPTER 4 TEST 2023-2024

1.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

2.

Find the sum.
(5x²-3x + 4) + (6x -3x²- 3)

a)

3x² + 2x + 1

b)

2x² + 3x +1

c)

2x² + 5x - 7

d)

3x²+ 4x⁵ -7x

3.

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

a)

3y³+ 7y²- 4y + 3

b)

4y² + 3y³ - y + 3

c)

-y⁴ + 2y³-y - 4

d)

4y³+ 3y²-3y + 1

4.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

5.

Simplify the expression:
(3x⁴ - 4 - 5x²) - (1 - x² + 2x³)

a)

3x⁴ - 2x³ - 4x² - 5

b)

3x⁴ - 7x³ - 4x² - 5

c)

3x⁴ - 7x³ - 4x² - 4

d)

3x⁴ - 5x³ - 4x² - 4

6.

Simplify the expression:
(p³ - 6p⁴ + 1) - (8p⁴ - 8p³ + 7)

a)

-14p⁴ + 9p³ - 6

b)

-14p⁴ + 9p³ + 6

c)

-14p⁴ + 9p³ - 1

d)

-15p⁴ + 9p³ + 6

7.

Simplify the expression:
(4a + 1 + 4a⁴) - (4a³ + 2a + 3a⁴)

a)

a⁴ - 4a³ + 3a + 7

b)

a⁴ - 7a³ + 3a + 7

c)

a⁴ - 4a³ + 3a + 1

d)

a⁴ - 4a³ + 2a + 1

8.

Simplify each expression.
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

9.

Simplify:

a)

9n³ + 4n

b)

7n³+ 6

c)

-3n³+ 2

d)

7n⁶ + 6

10.

Simplify:

a)

-5a⁶- 5a⁴

b)

-3a³ - 1a²

c)

-2a³ - 6a²

d)

5a³ - 5a²

11.

Simplify:

a)

0

b)

-3n³ +8n

c)

-3n⁶

d)

-6n³

12.

Solve the following problem.
(13x + 30) - (20x + 6)

a)

-7x + 24

b)

-33x - 42

c)

133x + 36

d)

260x + 180

13.

Solve the following problem.
(9x + 17) + (19x - 27)

a)

28x + 44

b)

28x - 10

c)

-28x + 10

d)

-171x - 459

14.

Solve the following problem.
(3x - 4) + (12x + 10)

a)

x - 12

b)

15x + 6

c)

36x + 40

d)

17x + 9,000

15.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

16.

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

a)

3y³+ 7y²- 4y + 3

b)

4y² + 3y³ - y + 3

c)

-y⁴ + 2y³-y - 4

d)

4y³+ 3y²-3y + 1

17.

Simplify the expression:
(p³ - 6p⁴ + 1) - (8p⁴ - 8p³ + 7)

a)

-14p⁴ + 9p³ - 6

b)

-14p⁴ + 9p³ + 6

c)

-14p⁴ + 9p³ - 1

d)

-15p⁴ + 9p³ + 6

18.

Simplify the expression:
(4v³ + 3v - 8v⁴) + (4v - 8v⁴ - 7)

a)

-17v⁴ + 4v³ + 2v - 7

b)

-16v⁴ + 4v³ + 10v - 7

c)

-16v⁴ + 4v³ + 7v - 7

d)

-16v⁴ + 4v³ + 2v - 7

19.

Simplify the expression:
(5b - 3b³ - 8b²) - (2b³ - 4b² + 6b - 3b⁴)

a)

3b⁴ - 5b³ - 11b² - b

b)

3b⁴ - 5b³ - 11b² - 9b

c)

3b⁴ - 5b³ - 11b² - 15b

d)

3b⁴ - 5b³ - 4b² - b

20.

Simplify the expression:
(7k + 2k³ - 8k⁴) - (4k³ - 5k + 4k² - 7k⁴⁾

a)

-k⁴ - 2k³ - 4k² + 12k

b)

-2k³ - 7k² + 12k + 4k⁴

c)

-2k³ - 4k³² + 12k + 4k⁴

d)

-2k³ - 4k² + 12k

21.

(x + 7)(x + 9)

a)

x² + 63x + 16

b)

x² + 16x + 63

c)

x² + 79

d)

x² + 16x + 2

22.

(x - 3)(x +10)

a)

x² - 7x + 13

b)

x² - 6x - 30

c)

x² + 7x - 30

d)

x² + 13x + 30

23.

(x + 5)(x + 4)

a)

x² + x + 20

b)

x² + 20x + 9

c)

x² + 9x + 20

d)

x² - 9x + 54

24.

(x +2)(x + 3)

a)

x² + 5x + 6

b)

x² + x + 6

c)

x² + 5x + 5

d)

x² + 6x + 6

25.

(x - 4)(x - 6)

a)

x² -10x + 24

b)

x² - 10x - 24

c)

x² +10x + 24

d)

x² + 10x - 24

26.

(x - 1)(x - 8)

a)

x² + 9x + 8

b)

x²+ 9x - 8

c)

x² - 9x - 8

d)

x² - 9x + 8

27.

(x + 12)(x - 12)

a)

x² - 144

b)

x² + 144

c)

x² + 12x - 144

d)

x² - 12x + 144

28.

(x - 7)(x + 7)

a)

x² + 7x - 49

b)

x² - 7x + 49

c)

x² - 49

d)

x² + 49

29.

Find the product:
(3x – 1)(x + 5)

a)

3x² + 4x + 5

b)

3x² + 4x - 5

c)

3x² + 14x + 5

d)

3x² + 14x - 5

30.

Simplify:
(x-7)²

a)

x²-49

b)

x²+49

c)

x²-14x+49

d)

x²-14x-49

31.

Find the product:
(3x + 2)(2x + 4)

a)

6x² + 16x + 8

b)

5x² +11x + 6

c)

5x² + 16x + 6

d)

6x² + 11x + 8

32.

(x + 5)²
Hint: try (x + 5)(x + 5)

a)

x² + 25

b)

x² + 10x + 25

c)

x² + 10 x + 10

d)

x² + 10

33.

Find the product:
(3x + 2)(2x + 4)

a)

6x² + 16x + 8

b)

5x² +11x + 6

c)

5x² + 16x + 6

d)

6x² + 11x + 8

34.

Find the Product.
(2x + 3)(2x - 3)

a)

4x² - 9

b)

4x² + 9

c)

4x²- 12x - 9

d)

4x² + 12x - 9

35.

Find the Product.
(2n + 3)(2n + 1)

a)

4n² + 8n + 3

b)

4n² - 8n - 3

c)

2n² + 8n - 3

d)

4n² - 8n + 3

36.

(x-3)(x²+2x+7)

a)

x³-x²+x-21

b)

x³+5x+13x-21

c)

x³-3x²+7x-21

d)

x²+2x-3

37.

Multiply the following together:

(2x + 3)(x² + 4x + 1)

a)

2x³ + 8x²+2x

b)

3x² + 12x +3

c)

2x³ +11x² +14x +3

d)

2x³ + 12x +3

38.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

39.

Simplify:
5(3x+2)

a)

3x+10

b)

15x+10

c)

15x-10

d)

3x-10

40.

Simplify:
2x ( -2x -3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

41.

4a(5a²- a + 4)

a)

20a³- 4a²+ 16a

b)

20a²- 5a + 8a

c)

20a²+ 4a²+ 16a

d)

20a³+3a² + 16a

42.

(3x - 5)(x² - 5x +6)

a)

3x³ - 20x² + 43x - 30

b)

3x^{2 -}- 43x

c)

3x³-25x -30

d)

3x³ +25x

43.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

44.

-5x⁶(3x² - 12x + 30)

a)

-15x⁸+ 60x⁷- 150x⁶

b)

15x⁸- 60x⁷- 150x⁶

c)

8x⁶- 17x + 35

d)

-8x⁶+ 17x - 35x²

45.

Multiply.
-3x²(7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

46.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

47.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

48.

(x-3)(x²+2x+7)

a)

x³-x²+x-21

b)

x³+5x+13x-21

c)

x³-3x²+7x-21

d)

x²+2x-3

49.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

50.

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

51.

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

52.

Find the Quotient
(2x³ - 5x² - 3x + 7) / (x - 2)

a)

2x²- 9x +15

b)

2x² - x - 5

c)

2x² - 9x - 21

d)

2x² + x + 5

53.

Find the remainder
(2x³ - 5x - 7) / (x + 2)

a)

-9

b)

11

c)

-13

d)

-1

54.

a)

5p²- 16p

b)

5p + 4

c)

5p - 4

d)

5p + 4p

55.

Divide:
(9x² + 6x) ÷ 3x

a)

3x + 2

b)

3x² + 2x

c)

5x²

d)

3x + 6

56.

Divide the polynomial by the monomial.

a)

15x⁹ - 8x³

b)

3x⁶ - 8x³

c)

-5x¹²

d)

3x⁶ - 40x³

57.

Find the quotient when (21x²- 52x + 32) is divided by (7x - 8).

a)

3x + 4

b)

3x + 3

c)

3x - 4

d)

3x + 2

58.

The area of a rectangular pool table is: x² + 14x +40.

The length is x + 4. What is the width?

a)

x + 8

b)

x + 14

c)

x + 10

d)

x +4

59.

Divide:
(24x + 4) / (6x+1)

a)

4

b)

4 + 4/6x+1

c)

4x + 0

d)

4x

60.

Divide:

(4x² - 24x + 35) / (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

61.

$\frac{x^2-12x+20}{x-2}$

a)

x+7

b)

x+2

c)

X-10

d)

X-7

62.

$\frac{2x^3+7x^2-6x-8}{x+4}$

a)

$2x^2-x-2$

b)

$2x^3-x^2-2x$

c)

$2x^2+15x+54+\frac{208}{x+4}$

d)

$2x^3+15x^2+54x+208$

63.

Use long division to solve: $\left(3y^5+5y^2-12y+10\right)\div\left(y^2+2\right)$

a)

$3y^3+6y^2+5y$

b)

$3y^4-6y^2+5$

c)

$3y^3-6y^2+5y-5$

d)

$3y^3-6y+5$

64.

Solve using long division. $\left(x^2+2x\ -\ 63\right)\div\left(x+9\right)$

a)

$x-7$

b)

$x^2-7$

c)

$x+7$

d)

$x^2+3x-54$

65.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect, and error occurs on the 2nd line!

c)

This is incorrect, and the error occurs on the 4th line!

d)

This is incorrect, and the error occurs on the 3rd line!

66.

Which term must be inserted in the dividend before you begin long division?

$\left(2x^3+5x^2+9\right)\div\left(x+3\right)$

a)

$0x^4$

b)

$0x^3$

c)

$0x^2$

d)

$0x$

67.

What is the remainder when you divide
$\left(2x^3-5x-7\right)\ by\ \left(x+2\right)$ ?

a)

-9

b)

11

c)

-13

d)

-1

68.

What do you call the number that you divide by?

a)

Quotient

b)

Divisor

c)

Remainder

d)

Factor

69.

Solve using long division. $\left(8x^2+6x-20\right)\div\left(4x-5\right)$

a)

$2x-4$

b)

$2x+4$

c)

$2x-1-\frac{16}{4x-5}$

d)

$2x-4-\frac{40}{4x-5}$

70.

Which term must be inserted in the dividend before you begin long division?

$\left(2x^3+5x^2+9\right)\div\left(x+3\right)$

a)

$0x^4$

b)

$0x^3$

c)

$0x^2$

d)

$0x$

71.

Identify the missing term to complete the solution.

a)

-7

b)

7

c)

-57

d)

57

72.

a)

This is correct

b)

This is incorrect

73.

a)

4x - 2

b)

4x + 2

c)

4x - 2 + (1/3x - 1)

d)

4x + 2 + (1/3x - 1)

74.

Divide
(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

75.

(27x³+ 9x²- 3x - 10) ÷ (3x - 2)

a)

9x⁴+5

b)

9x²+9x+5

c)

9x²-9x+5

d)

9x²-9x

76.

Solve using long division $\left(2x^2+6x-20\right)\div\left(2x-4\right)$

a)

$x+5+\frac{2}{2x-4}$

b)

$x-8$

c)

$x-5+\frac{3}{2x-4}$

d)

$x+5$

77.

Solve using long division. $\left(8x^2+6x-20\right)\div\left(4x-5\right)$

a)

$2x-4$

b)

$2x+4$

c)

$2x-1-\frac{16}{4x-5}$

d)

$2x-4-\frac{40}{4x-5}$

78.

Find the quotient when (21x²- 52x + 32) is divided by (7x - 8).

a)

3x + 4

b)

3x + 3

c)

3x - 4

d)

3x + 2

79.

Divide (x² + 5x - 8) by (x + 3). What is the remainder?

a)

16

b)

12

c)

-14

d)

-16

80.

a)

2x - 5

b)

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

c)

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

d)

2x + 4

81.

a)

-3x² + 3x + 2

b)

x² - 3x - 2

c)

-3x²+ 2

d)

x² + 3x + 2

82.

a)

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

b)

x - 8

c)

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

d)

x + 5

83.

(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

84.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

85.

(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

86.

(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

87.

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

88.

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

89.

4x⁴+4x³-9x²-x+2 ÷ x-1

a)

4x³+8x²-7x-2

b)

4x³+19x²-x-2

c)

4x³+8x²-x-9

d)

4x³+8x²-x-2

90.

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

a)

0

b)

1

c)

2

d)

3

91.

(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

92.

(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

93.

x³-3x²-10x+24 ÷ x+3

a)

x²-7x+5

b)

x-8

c)

x²-6x+8

d)

x+9

94.

-2x²+4x+48 ÷ x+4

a)

-2x+12

b)

2x+12

c)

-4x+9

d)

4x+9

95.

Use synthetic division:
(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

96.

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.

97.

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

98.

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

99.

4x⁴+4x³-9x²-x+2 ÷ x-1

a)

4x³+8x²-7x-2

b)

4x³+19x²-x-2

c)

4x³+8x²-x-9

d)

4x³+8x²-x-2

100.

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

a)

0

b)

1

c)

2

d)

3

101.

Use synthetic division:
(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

102.

Use any style of division to simplify: $\frac{x^5-3x^4+2x^3-x^2+9x+3}{x-2}$

a)

$x^4-x^3-x+7+\frac{17}{x-2}$

b)

$x^4-x^3-x^2+7x+17$

c)

$x^4-5x^3+12x^2-25x+59+\frac{121}{x-2}$

d)

$x^4+x^3+x-7-\frac{17}{x-2}$

103.

Use any style of division to simplify: $\frac{x^5-3x^4+2x^3-x^2+9x+3}{x-2}$

a)

$x^4-x^3-x+7+\frac{17}{x-2}$

b)

$x^4-x^3-x^2+7x+17$

c)

$x^4-5x^3+12x^2-25x+59+\frac{121}{x-2}$

d)

$x^4+x^3+x-7-\frac{17}{x-2}$

104.

Use any style of division to simplify: $\frac{x^4+x^3+2x^2+3x+9}{x+1}$

a)

$x^3+2x+1+\frac{8}{x+1}$

b)

$x^3+2x^2+4x+7+\frac{16}{x+1}$

c)

$x^3+2x^2+x+8$

d)

$x^3-2x-1-\frac{8}{x+1}$

105.

Use any style of division to simplify: $\frac{x^5-x^3+2x+4}{x+2}$

a)

$x^4-2x^3+3x^2-6x+14-\frac{24}{x+2}$

b)

$x^4+2x^3+3x^2+6x+14+\frac{32}{x+2}$

c)

$x^4-2x^3-3x^2-6x-14-\frac{32}{x+2}$

d)

$x^4+2x^3-3x^2+6x-14+\frac{24}{x+2}$

106.

Use any style of division to simplify: $\frac{x^6-1}{x+1}$

a)

$x^5-x^4+x^3-x^2+x-1$

b)

$x^5+x^4+x^3+x^2+x+1$

c)

$x^5+x^4+x^3-x^2-x-1$

d)

$x^5-x^4-x^3+x^2+x+1$

107.

Use any style of division to simplify: $\frac{x^3+3x^2-9x+10}{x+4}$

a)

$x^2-x-5+\frac{30}{x+4}$

b)

$x^2+7x+19+\frac{86}{x+4}$

c)

$x^2-7x-19-\frac{86}{x+4}$

d)

$x^2+x+5-\frac{30}{x+4}$

108.

True or False:

When you do a polynomial division, and the remainder is 0, that means that the denominator is a factor of the numerator.

a)

TRUE

b)

FALSE

109.

Let f(x) = 3x² - 9x +2.
Is k = -3 a zero of the function?

a)

yes

b)

no

110.

Let f(x) = 4x² -33x -27. Is k = 9 a zero of the function?

a)

yes

b)

no

111.

When p(x) = 9x⁴- 45x³+ 37x² + x +2 is divided by x - 2, a student can determine the remainder by evaluating p(2). What is the value of p(2)?

a)

p(2) = 656

b)

p(2) = 652

c)

p(2) = -64

d)

p(2) = -368

112.

a)

A

b)

B

c)

C

d)

D

113.

a)

A

b)

B

c)

C

d)

D

114.

a)

A

b)

D

c)

C

d)

D

115.

a)

A

b)

B

c)

C

d)

D

116.

a)

A

b)

B

c)

C

d)

D

117.

a)

A

b)

B

c)

C

d)

D

118.

a)

A

b)

B

c)

C

d)

D

119.

a)

A

b)

B

c)

C

d)

D

120.

a)

A

b)

B

c)

C

d)

D

121.

if f(x) = 3x² -9x -20, find the value of f(5) using synthetic division.

a)

0

b)

10

c)

15

d)

-7

122.

Factor:
x² - 5x - 14

a)

(x - 2)(x + 3)

b)

(x - 2)(x + 7)

c)

(x + 2)(x - 7)

d)

(x - 2)(x - 3)

123.

Which of the following is a factor of x²-10x+24?

a)

x-4

b)

x+4

c)

x+6

d)

x-2

124.

Solve by factoring: x² + 3x - 18 = 0

a)

x = -3 and x = 6

b)

x = 3 and x = -6

c)

x = -9 and x = 2

d)

x = 9 and x = -2

125.

x² - 6x - 7 = 0

a)

{-1, 7}

b)

{-3, -1}

c)

{5, 6}

d)

{-3, 3}

126.

Factor Completely:
3x² + 18x +15

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

127.

3x²+9x-30=0

a)

x= 2, -5

b)

x= 5, -2

c)

x= -5, -2

128.

Factor:
2x² + 11x + 14

a)

(x + 7)(2x + 2)

b)

(x + 2)(2x + 7)

c)

(x + 14)(2x + 1)

d)

(x + 1)(2x + 14)

129.

Solve by factoring: 5x² + 13x + 6 = 0

a)

x = -2 and x = -3/5

b)

x = 2 and x = 3/5

c)

x = -2 and x = 3/5

d)

x = 2 and x = -3/5

130.

Factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

131.

$x^2-100=0$

a)

$\left\{25,4\right\}$

b)

$\left\{-50,2\right\}$

c)

$\left\{-10,10\right\}$

d)

$\left\{0,100\right\}$

132.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

133.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

134.

Factor
n² + 5n - 6

a)

(n - 2)(n - 3)

b)

(n - 1)(n + 6)

c)

(n + 1)(n - 6)

d)

(n + 2)(n - 3)

135.

Factor
a² - a - 12

a)

(a - 4)(a + 3)

b)

(a + 6)(a - 4)

c)

(a - 6)(a + 4)

d)

(a + 4)(a - 3)

136.

Factor
r² -16r + 60

a)

(r - 15)(r + 4)

b)

(r - 6)(r + 10)

c)

(r - 6)(r - 10)

d)

(r +30)(r - 2)

137.

Factor:
x²-15x + 36

a)

(x - 18)(x + 2)

b)

(x - 12)(x - 3)

c)

(x - 12)(x + 3)

d)

(x + 18)(x - 2)

138.

What are the factors of
25x² - 81?

a)

(5x - 9)(5x + 9)

b)

(5x - 9)(5x - 9)

c)

(5x + 9)(5x + 9)

d)

Cannot be factored

139.

Factor
a² - a - 12

a)

(a - 4)(a + 3)

b)

(a + 6)(a - 4)

c)

(a - 6)(a + 4)

d)

(a + 4)(a - 3)

140.

Factor:
2x² - 3x - 2

a)

(2x - 2)(x + 1)

b)

(2x + 1)(x - 2)

c)

(2x - 1)(x - 2)

d)

(2x - 1) (x - 1)

141.

Factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

142.

Factor
x² + 11x + 24

a)

(x + 6)(x + 4)

b)

(x + 10)(x + 2)

c)

(x + 8)(x + 3)

d)

(x + 2)(x + 12)

143.

Factor completely.
3x² + 10x - 8

a)

(3x + 2)(x + 4)

b)

(7x + 5)(x + 2)

c)

(3x - 2)(x + 4)

d)

(7x - 3)(x - 4)

144.

Factor completely.
5x² - 7x + 2

a)

5(x - 2)(x + 1)

b)

(5x - 2)(x + 1)

c)

(7x - 1)(x - 4)

d)

(5x - 2)(x - 1)

145.

Factor:
x² - 9

a)

(x + 3)(x - 3)

b)

(x + 3)²

c)

(x - 3)²

d)

(x+3)(x+3)

146.

How many terms are in

$3x^2\ +4x\ -\ 5$

a)

1

b)

2

c)

3

d)

None

147.

What is the leading Coefficient in

$6y^4-5y^2+5x\ -7$

a)

-5

b)

5

c)

6

d)

-7

148.

Classify the polynomial below by degree

$5x^3-4x^2+2x-8$

a)

cubic

b)

quadratic

c)

quartic

d)

linear

149.

Classify the polynomial below by terms

$6x-2$

a)

linear

b)

quadratic

c)

binomial

d)

trinomial

150.

Classify the polynomial below by degree and terms

$x^2-4x-1$

a)

quadratic, trinomial

b)

linear, trinomial

c)

quartic, binomial

d)

cubic, trinomial

151.

Classify the polynomial by degree

$5x-1$

a)

quadratic

b)

linear

c)

binomial

d)

constant

152.

Classify the polynomial by degree and terms

6

a)

constant, monomial

b)

linear, monomial

c)

quadratic, binomial

d)

Can't be classified

153.

Put the polynomial in standard form

$6x\ -\ 4x^2+2\ -\ 5x^3$

a)

$-5x^3-4x^2+6x+2$

b)

$-4x^2+6x-5x^3+2$

c)

$-5x^3-6x+4x^2+2$

d)

it is in standard form

154.

What is the constant in

$7y^4-5x^3+9y^2-8x+4$

a)

7

b)

-5

c)

-8

d)

4

155.

Which polynomial is a quadratic binomial?

a)

$9m^2-3$

b)

7x+2

c)

$2x^3-5$

d)

$y^2+4x-1$

156.

How many terms does this polynomial have?

a)

$0$

b)

$1$

c)

2

d)

3

157.

Classify this polynomial by the number of its terms.

a)

monomial

b)

binomial

c)

trinomial

d)

quadnomial

158.

This polynomial is degree _________.

a)

0

b)

1

c)

2

d)

3

159.

What is the constant term of this polynomial?

a)

7

b)

2

c)

3

d)

9

e)

-9

160.

What is the leading term of this polynomial?

a)

$7b^2$

b)

7

c)

b

d)

9

e)

-9

161.

What is the leading coefficient of this polynomial?

a)

$7b^2$

b)

7

c)

b

d)

9

e)

-9

162.

Classify this polynomial by degree?

a)

constant

b)

linear

c)

quadratic

d)

cubic

e)

quartic

163.

Rewrite this polynomial in standard form.

$6x-2x^2+5$

a)

$2x^2-6x+5$

b)

$2x^2+6x+5$

c)

$5+6x-2x^2$

d)

$-2x^2+6x+5$

164.

Classify this polynomial.

$12x^2$

a)

Linear monomial

b)

quadractic monomial

c)

cubic monomial

d)

quadratic binomial

165.

Name the constant in this polynomial.

$4x^2-7x+6-x^3$

a)

4

b)

7

c)

6

d)

1

e)

-1

166.

What is the degree of this polynomial.

$4x^2-7x+6-x^3$

a)

0

b)

1

c)

2

d)

3

e)

4

167.

Classify this polynomial by degree.

$4x^2-7x+6-x^3$

a)

constant

b)

linear

c)

quadratic

d)

cubic

e)

quartic

168.

After writing this polynomial in standard form, what is the leading term?

$4x^2-7x+6-x^3$

a)

$4x^2$

b)

1

c)

-1

d)

$-x^3$

e)

$x^3$

169.

After writing this polynomial in standard form, what is the leading coefficient?

$4x^2-7x+6-x^3$

a)

4

b)

1

c)

-1

d)

$-x^3$

e)

$4x^2$

170.

Classify this polynomial by degree and number of terms.

$2+3x$

a)

linear binomial

b)

quadratic binomial

c)

cubic binomial

d)

quadratic trinomial

171.

What is the leading coefficient of this polynomial?

$2+3x$

a)

1

b)

2

c)

3

d)

4

172.

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

a)

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

b)

f(x) =x³ - 3x² - 6x + 8

c)

f(x) = x³+ 8

d)

f(x) = x³ - 3x² + 8

173.

Write a polynomial function of least degree with integral coefficients that has the given zeros.

a)

A

b)

B

c)

C

d)

D

174.

Write a polynomial function of least degree with integral coefficients that has the given zeros.

a)

A

b)

B

c)

C

d)

D

175.

Write the polynomial with the given zeros

a)

A

b)

B

c)

C

d)

D

176.

For the following problem write the simplest polynomial function with the given zeros: 2, -1, and -8

a)

$x^3\ +7x^2\ +10x\ +16$

b)

$x^3\ +7x^2\ +10x\ -16$

c)

$x^3\ +7x^2\ -10x\ -16$

d)

$x^3\ -7x^2\ -10x\ -16$

177.

For the following problem write the simplest polynomial function with the given zeros: 2, -1, and -8

a)

$x^3\ +7x^2\ +10x\ +16$

b)

$x^3\ +7x^2\ +10x\ -16$

c)

$x^3\ +7x^2\ -10x\ -16$

d)

$x^3\ -7x^2\ -10x\ -16$

178.

Write the equation of the quadratic

whose roots are -4, -2.

a)

x²-6x+8

b)

x²+6x+8

c)

x²-4x-2

d)

x²-2x-4

179.

Write a polynomial function of least degree with integral coefficients and have zeros 3, - 1, 1, 2

a)

x⁴ - 5x³ + 5x² + 5x - 6

b)

x⁴ + 5x³ + 5x² + 5x - 6

c)

x⁴ - 5x³ - 5x² + 5x - 6

d)

x⁴ - 5x³ + 5x² + 5x + 6

180.

Write a polynomial function of least degree with integral coefficients and have zeros 4, - 1, 6

a)

x³ + 9x² + 14x + 24

b)

x³ - 9x² + 14x - 24

c)

x³ - 9x² + 14x + 24

d)

x³ - 9x² - 14x + 24

181.

Write a polynomial function of least degree with integral coefficients and have zeros 2, 1, -1.

a)

x³ - 2x² - x + 2

b)

x³ + 2x² - x + 2

c)

x³ - 2x² - x - 2

d)

x³ - 2x² + x + 2

182.

Build a Polynomial with the following Zeros:

-1, 4

a)

x² - 3x - 4

b)

x² + 3x + 4

c)

x² - 5x + 5

d)

x² - 5x - 4

183.

Write the equation of the quadratic

whose roots are -4, -2.

a)

x²-6x+8

b)

x²+6x+8

c)

x²-4x-2

d)

x²-2x-4

184.

Write the equation for a parabola

that opens downward whose zeros are x = 1, x = 3.

a)

x²-4x+3

b)

x²+4x+3

c)

-x²+4x-3

d)

-x²-4x-3

185.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

a)

±1, ±8

b)

±1, ±2, ±4, ±8

c)

±1, ±2, ±4

d)

1, 2, 4, 8

186.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 3x³ + 2x² - 6x + 7

a)

±1, ±7, ±1/3, ±7/3

b)

±1, 7

c)

±1, ±3, ±7, ±7/3

d)

±1, ±3, ±7, ±1/3, ±7/3

187.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 2x³ + 5x² - 9x + 5

a)

±1, ±5, ±1/2, ±5/2

b)

±1, ±2, ±5, ±1/2, ±5/2

c)

±1, ±5

d)

±1, ±2, ±5, ±1/2, ±5/2, ±2/5

188.

Solve by using Rational Root Theorem:
2x³ - 11x² + 12x + 9 = 0

a)

-1, 1, 3

b)

-1, 3/2, 3

c)

-1/2, 3, 3

d)

-1/2, 1, 3

189.

Solve by using Rational Root Theorem:
x³ - 7x - 6 = 0

a)

1, 2, 3

b)

-1, -2, - 3

c)

-1, -2, 3

d)

1,-2,-3

190.

According to the Rational Root Theorem, what are the all possible rational roots?
2x³ - 11x² + 12x + 9 = 0

a)

±1,±2

b)

±1,±3,±9

c)

±1,±3±9,±1/2,±3/2,±9/2

d)

±1,±2,±1/3,±2/3,±1/9,±2/9

191.

Solve by using Rational Root Theorem:
x³ + 3x² - 6x - 8 = 0

a)

-4, -1, 2

b)

-4, -1, ±√2

c)

1, 2, 4

d)

4,-1,√2

192.

Below are four possible zeros for this polynomial.

Figure out which one "works"

f(x) = x³ + 2x² - 11x - 12

a)

-3

b)

-4

c)

1

d)

6

193.

Below are four possible zeros for this polynomial.

Figure out which one "works"

f(x) = x³ - 8x² - 23x + 30

a)

3

b)

-1

c)

-10

d)

1

194.

What are the zeros of the polynomial?

h(x) = x⁴ + 3x³ - 55x² - 99x +630

a)

-5,6,-3,7

b)

5 6, 3, -7

c)

-5, 6, 3, -7

d)

6, 3, -7

195.

What are the zeros of the polynomial

g(x) = 2x⁴ -19x² + 46x² + 7x - 60

a)

-1,4,5,3/2

b)

-1,-4,5,-3/2

c)

1,4,5,3/2

d)

-1,4,5,2/3

196.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

a)

±1, ±8

b)

±1, ±2, ±4, ±8

c)

±1, ±2, ±4

d)

1, 2, 4, 8

197.

Use the Complex Conjugate Root Theorem to state another complex solution. Given that 3+5i is a root.

a)

-3+5i

b)

-3-5i

c)

-5i

d)

3-5i

198.

Use the Complex Conjugate Root Theorem to state another complex solution. Given that -2-5i is a root.

a)

-2-5i

b)

-2+5i

c)

2+5i

d)

5i

199.

Which of the following would be the correct factored form with roots 2, 5i, and 6?

a)

(x-6)(x-2)(x+5i)(x-5i)

b)

(x+6)(x+2)(x+5i)

c)

(x-6)(x-2)(x-5i)

d)

(x+6)(x+2)(x-5i)

200.

If a+bi is a root of a polynomial, then _______ is also a root.

a)

i²

b)

a-bi

c)

a+bi

d)

-i²

201.

Write in factored form using the following roots.

7, -2i

a)

(x-7)(x-2i)

b)

(x-7)(x+2i)(x-2i)

c)

(x-7)(x+2i)

d)

(x-7)(x+7)(x-2i)

202.

Expand into standard form.

(x-7)(x-4)

a)

x²-4x+28

b)

x²-11x+7

c)

x²-11x+28

d)

x²-7x+28

203.

Expand into standard form

(x+2i)(x-2i)

a)

x²-4

b)

x²+4

c)

x+2i²

d)

x²+2i²

204.

Write a polynomial function of least degree with the given zeros.

a)

A

b)

B

c)

C

d)

D

205.

Write a polynomial function of least degree with the given zeros.

a)

A

b)

B

c)

C

d)

D

206.

Write a polynomial function of least degree with the given zeros.

a)

A

b)

B

c)

C

d)

D

207.

How many possible negatives solutions does the following polynomial have?

f(x) = x⁴ - 3x³ - 17x² + 39x -20

a)

3 or 1

b)

3

c)

1

d)

2 or 0

208.

How many positive solutions does the following polynomial have?

f(x) =3x⁵ - x⁴ + 3x² - 6x +11

a)

4, 2, or 0

b)

4

c)

3 or 1

d)

3

209.

How many possible negatives solutions does the following polynomial have?

f(x) = x⁴ - 3x³ - 17x² + 39x -20

a)

3 or 1

b)

3

c)

1

d)

2 or 0

210.

How many positive solutions does the following polynomial have?

f(x) =3x⁵ - x⁴ + 3x² - 6x +11

a)

4, 2, or 0

b)

4

c)

3 or 1

d)

3

211.

Use Descartes Rule of Signs to determine the possible number of positive and negative roots.

a)

1 positive, 2 or 0 negative

b)

1 positive, 1 negative

c)

0 positive, 1 negative

d)

1 positive, 0 negative

212.

Use Descartes Rule of Signs to determine the possible number of positive and negative roots.

a)

3 or 1 positive roots and 0 negative roots

b)

4, 2, or 0 positive roots and 1 negative root

c)

4, 2, or 0 positive roots and 0 negative roots

d)

2 or 0 positive roots and 1 negative roots

213.

Find the zeros of the polynomial given one factor. Use synthetic division.

a)

X= 3,4,5

b)

x=-3,-4,-5

c)

x=-3,4,5

d)

x= 3, -4, -5

214.

Find all zeros. Do not use the calculator.

a)

x= 3,1,1/3

b)

x= -3, -1, -1/3

c)

x = -3, 1, 1/3

d)

x = 3, -1, -1/3

215.

Using Descartes' Rule of Signs, how many possible NEGATIVE roots are there for the polynomial f(x) = x⁴+x³+x²+x+5. Select all that apply.

a)

0

b)

1

c)

2

d)

3

e)

4

216.

Write a polynomial function with rational coefficients that has zeros - 4 and 5i.

a)

P(x) = x³ + 4x² + 25x + 100

b)

P(x) = 5x³ - 4x² + 25x + 100

c)

P(x) = x³ + x² - 25x + 100

d)

P(x) = 4x² + 5

A2-CHAPTER 4 TEST 2023-2024

Total questions: 216

Worksheet time: 17hrs 15mins