Free Printable Alg2 - Test 6 - Factoring Quadratic Expressions and Equations

1.

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

2.

Factor completely.
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

3.

Factor completely:
3x² + 5x - 12

a)

(3x + 4)(x-3)

b)

(3x - 4)(x + 3)

c)

(3x + 3)(x -4)

d)

(3x - 3)(x + 4)

4.

Factor completely: 2x²+22x+60

a)

(2x+10)(x+6)

b)

(x+5)(x+6)

c)

2(x+1)(x+30)

d)

2(x+5)(x+6)

5.

Factor completely: x²-6x+8

a)

(x-2)(x-4)

b)

(x-1)(x-8)

c)

(x+2)(x+4)

d)

(x+1)(x+8)

6.

Factor completely: x²+16x+64

a)

(x+4)(x+16)

b)

(x-8)(x-8)

c)

(x+2)(x+32)

d)

(x+8)(x+8)

7.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

8.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

9.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

10.

Factor
9x²+9x-10

a)

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

b)

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

c)

(3x+5)(3x+2)

d)

Not Factorable

11.

Factor:
p² - 14p

a)

p(1 - 14)

b)

2p(p - 7)

c)

p²(1-14)

d)

p(p - 14)

12.

Which is another way of correctly expressing
(x - 3)(x - 3)?

a)

(x² - 3²)

b)

(x² - 3)

c)

(x + 3)(x - 3)

d)

(x - 3)²

13.

x²- 16

a)

Prime

b)

( x - 4) ( x + 4)

c)

( x - 8) ( x + 8)

d)

( x - 4) ( x - 4)

14.

Which answer choice lists all the factors for 27?

a)

3, 9

b)

1, 3, 9, 27

c)

1, 3, 6, 9, 12, 27

15.

Factor Completely:
2k²-14k-60

a)

2(k-10)(k-3)

b)

Not Factorable

c)

(k-5)(k+9)

d)

2(k-10)(k+3)

16.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

17.

Factor
a² - a - 12

a)

(a - 4)(a + 3)

b)

(a + 6)(a - 4)

c)

(a - 6)(a + 4)

d)

(a + 4)(a - 3)

18.

Factor
k²+7k+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

19.

The trinomial 4x²-20x + 25 is factorable.

Which of these is the correct factorization?

a)

(2x+5)(2x-5)

b)

$\left(2x-5\right)\left(2x-5\right)\ Or\ \left(2x-5\right)^2$

c)

$\left(2x+5\right)\left(2x+5\right)\ Or\ \ \left(2x+5\right)^2$

d)

$\left(x-5\right)\left(4x-5\right)$

20.

Factor:

2x² + 3x - 9

a)

2(x + 3)(x - 3)

b)

(2x - 3)²

c)

(x + 3)(2x - 3)

d)

(2x + 3)(x - 3)

21.

Find the factors of

3b² + 17b + 20

a)

(2b - 5)(b - 7)

b)

(5b - 7)(b - 2)

c)

(b + 5)(3b + 4)

d)

(3b + 5)(b + 4)

22.

Find the factors of

2x² + 21x + 10

a)

(2x + 1)(x + 10)

b)

(3x + 10)(x - 6)

c)

2(x + 1)(x + 5)

d)

2(x + 1)(x - 10)

23.

x² − 7x − 18

a)

(x − 9)(x + 2)

b)

(x + 9)(x + 2)

c)

(x − 9)(x - 2)

d)

(x − 9)(x - 2)

24.

p² − 5p − 14

a)

( p + 2)( p + 7)

b)

( p + 2)( p − 7)

c)

( p - 2)( p − 7)

d)

( p - 2)( p + 7)

25.

m² − 9m + 8

a)

(m + 1)(m − 8)

b)

(m − 1)(m + 8)

c)

(m − 1)(m − 8)

d)

(m + 1)(m + 8)

26.

x² − 16x + 63

a)

(x + 9)(x + 7)

b)

(x − 9)(x + 7)

c)

(x + 9)(x − 7)

d)

(x − 9)(x − 7)

27.

7x² − 31x − 20

a)

(7x + 4)(x − 5)

b)

(7x - 4)(x − 5)

c)

(7x + 4)(x + 5)

d)

(7x - 4)(x − 5)

28.

7k² + 9k

a)

k(7k - 9)

b)

k(7k + 9)

c)

7k(k + 9)

d)

(k+3)(7k + 3)

29.

7x² − 45x − 28

a)

7(x + 4)(x − 7)

b)

(x + 4)(7x - 7)

c)

(7x + 4)(x − 7)

d)

(7x - 4)(x + 7)

30.

2b² + 17b + 21

a)

(2b + 7)(b + 3)

b)

(2b + 3)(b - 7)

c)

2(b + 3)(b + 7)

d)

(2b + 3)(b + 7)

31.

5p² − p − 18

a)

5(p + 9)( p − 2)

b)

(p + 9)( 5p − 2)

c)

(5p - 9)( p + 2)

d)

(5p + 9)( p − 2)

32.

28n⁴ + 16n³ − 80n²

a)

4n² (7n + 10)(n - 2)

b)

(28n² − 10)(n² + 2)

c)

4n² (7n − 10)(n + 2)

d)

(7n − 10)(4n² + 2)

33.

3b³ − 5b² + 2b

a)

b(3b − 2)(b − 1)

b)

(3b² − 2)(b − 1)

c)

(3b − 2)(b² − 1)

d)

b(3b + 2 )(b + 1)

34.

7x² − 32x − 60

a)

(7x + 10)(x − 6)

b)

7(x + 10)(x − 6)

c)

(7x - 10)(x − 6)

d)

(7x - 10)(x + 6)

35.

30n²b − 87nb + 30b

a)

(6nb − 5)(5n − 2)

b)

3n(2b − 5)(5n − 2)

c)

3b(2n − 5)(5n + 2)

d)

3b(2n − 5)(5n − 2)

36.

9r² − 5r − 10

a)

(9r + 2)(r - 5)

b)

(3r + 2)(3r - 5)

c)

9(r + 2)(r - 5)

d)

not factorable

37.

9p²r + 73pr + 70r

a)

r(p + 7)(9p + 10)

b)

(rp + 7)(9p + 10)

c)

r(3p + 7)(3p + 10)

d)

p(r + 7)(9r + 10)

38.

9x² + 7x − 56

a)

(3x + 7)(3x - 8)

b)

9(x + 7)(x - 8)

c)

(3x - 7)(3x - 8)

d)

not factorable

39.

10m² + 89m − 9

a)

(m + 9)(10m + 1)

b)

(m + 9)(10m − 1)

c)

(m - 9)(10m − 1)

d)

not factorable

40.

4x³ + 43x² + 30x

a)

x(x + 10)(4x + 3)

b)

(x² + 10)(4x + 3)

c)

x(x + 3)(4x + 10)

d)

(x + 10)(4x + 3)

41.

Factor:

$x^2-10x-24$

a)

$(x+2)(x+12)$

b)

$(x+3)(x-8)$

c)

$(x+2)(x-12)$

d)

Not factorable

42.

Factor:

$n^2-20n+84$

a)

$(n+28)(n+3)$

b)

$(n+6)(n+14)$

c)

$(n+6)(n-14)$

d)

$(n-6)(n-14)$

43.

Factor:

$-2n^3-70n^2-600n$

a)

$-2n(n+15)(n+20)$

b)

$-2n(n+15)(n-20)$

c)

$-2(n-15)(n-20)$

d)

$-2n(n+12)(n+25)$

44.

Factor:

$-5a^2-95a-90$

a)

$-5(a+6)(a+3)$

b)

$-5(a-1)(a+18)$

c)

$-5(a+1)(a+18)$

d)

$-5(a-1)(a-18)$

45.

Factor:

$2n^2-55n+342$

a)

$(2n+19)(n+18)$

b)

$2(n+3)(n+57)$

c)

$(2n-19)(n-18)$

d)

$2(n-19)(n+9)$

46.

Factor:

$19b^2-362b-360$

a)

$(b+18)(19b-20)$

b)

$(19b+18)(b-20)$

c)

$(19b+18)(b+20)$

d)

Not factorable

47.

Factor:

$a^2+12a-45$

a)

$(a-3)(a-15)$

b)

$(a+45)(a-1)$

c)

$(a-3)(a+15)$

d)

Not factorable

48.

Factor:

$11v^3-165v^2+396v$

a)

$11v(v-3)(v-12)$

b)

$11v(v+3)(v-12)$

c)

$11(v+6)^2$

d)

$11v(v-3)(v+12)$

49.

Factor:

$5b^2-63b+162$

a)

$(11b+16)(b-14)$

b)

$(5b-18)(b-9)$

c)

$(5b+18)(b-9)$

d)

Not factorable

50.

Factor:

$k^2-9k+14$

a)

$(k+3)(k-7)$

b)

$(k-2)(k-7)$

c)

$(k-2)(k+7)$

d)

$(k-9)(k+10)$

51.

Factor:

$x^2+x-90$

a)

Not factorable

b)

$(x-9)(x+10)$

c)

$(x+18)(x-5)$

d)

$(x-9)(x-10)$

52.

Factor:

$-5v^2+15v+350$

a)

$-5(v-10)(v-7)$

b)

$-5(v+10)(v-7)$

c)

$-5(v-10)(v+7)$

d)

$-5(v+10)(v+7)$

53.

Factor:

$-3m^2+12m+36$

a)

$-3(m-6)(m-2)$

b)

$-3(m+6)(m-2)$

c)

$-3(m-6)(m+2)$

d)

$-3(m+3)(m-4)$

54.

Factor:

$5x^3+5x^2-100x$

a)

$5x(x+4)(x-5)$

b)

$5x(x-4)(x-5)$

c)

$5x(x-4)(x+5)$

d)

$5(x+4)(x-5)$

55.

Factor:

$5v^2+32v-64$

a)

$(5v-8)(v+8)$

b)

$(5v+8)(v-8)$

c)

$(5v+32)(v-2)$

d)

$5(v-8)^2$

56.

Factor:

$5a^2-48a+27$

a)

$(5a+27)(a+1)$

b)

$(5a+3)(a+9)$

c)

$(5a-3)(a-9)$

d)

$(2a-9)(a+6)$

57.

Factor:

2p^2+p-45

a)

Not factorable

b)

$(2p+5)(p+2)$

c)

$(2p-9)(p+5)$

d)

$(2p+15)(p-3)$

58.

Factor:

$a^2+7a-8$

a)

$(a+1)(a+8)$

b)

$(a+1)(a-8)$

c)

$(a-1)(a-8)$

d)

$(a-1)(a+8)$

59.

Factor:

$6k^3+36k^2-96k$

a)

$6(k-2)(k-8)$

b)

$-3k(k+2)(k-5)$

c)

$6k(k-2)(k-8)$

d)

$6k(k-2)(k+8)$

60.

Factor:

$3k^2-28k+60$

a)

$3(k-10)(k+6)$

b)

$3(k-10)(k+2)$

c)

$(3k-10)(k-6)$

d)

$(3k+10)(k+6)$

61.

Factor:

$x^2-10x-24$

a)

$(x+2)(x+12)$

b)

$(x+3)(x-8)$

c)

$(x+2)(x-12)$

d)

Not factorable

62.

Factor:

$n^2-20n+84$

a)

$(n+28)(n+3)$

b)

$(n+6)(n+14)$

c)

$(n+6)(n-14)$

d)

$(n-6)(n-14)$

63.

Factor:

$-2n^3-70n^2-600n$

a)

$-2n(n+15)(n+20)$

b)

$-2n(n+15)(n-20)$

c)

$-2(n-15)(n-20)$

d)

$-2n(n+12)(n+25)$

64.

Factor:

$-5a^2-95a-90$

a)

$-5(a+6)(a+3)$

b)

$-5(a-1)(a+18)$

c)

$-5(a+1)(a+18)$

d)

$-5(a-1)(a-18)$

65.

Factor:

$2n^2-55n+342$

a)

$(2n+19)(n+18)$

b)

$2(n+3)(n+57)$

c)

$(2n-19)(n-18)$

d)

$2(n-19)(n+9)$

66.

Factor:

$19b^2-362b-360$

a)

$(b+18)(19b-20)$

b)

$(19b+18)(b-20)$

c)

$(19b+18)(b+20)$

d)

Not factorable

67.

Factor:

$a^2+12a-45$

a)

$(a-3)(a-15)$

b)

$(a+45)(a-1)$

c)

$(a-3)(a+15)$

d)

Not factorable

68.

Factor:

$11v^3-165v^2+396v$

a)

$11v(v-3)(v-12)$

b)

$11v(v+3)(v-12)$

c)

$11(v+6)^2$

d)

$11v(v-3)(v+12)$

69.

Factor:

$5b^2-63b+162$

a)

$(11b+16)(b-14)$

b)

$(5b-18)(b-9)$

c)

$(5b+18)(b-9)$

d)

Not factorable

70.

Factor:

$k^2-9k+14$

a)

$(k+3)(k-7)$

b)

$(k-2)(k-7)$

c)

$(k-2)(k+7)$

d)

$(k-9)(k+10)$

71.

Factor:

$x^2+x-90$

a)

Not factorable

b)

$(x-9)(x+10)$

c)

$(x+18)(x-5)$

d)

$(x-9)(x-10)$

72.

Factor:

$-5v^2+15v+350$

a)

$-5(v-10)(v-7)$

b)

$-5(v+10)(v-7)$

c)

$-5(v-10)(v+7)$

d)

$-5(v+10)(v+7)$

73.

Factor:

$-3m^2+12m+36$

a)

$-3(m-6)(m-2)$

b)

$-3(m+6)(m-2)$

c)

$-3(m-6)(m+2)$

d)

$-3(m+3)(m-4)$

74.

Factor:

$5x^3+5x^2-100x$

a)

$5x(x+4)(x-5)$

b)

$5x(x-4)(x-5)$

c)

$5x(x-4)(x+5)$

d)

$5(x+4)(x-5)$

75.

Factor:

$5v^2+32v-64$

a)

$(5v-8)(v+8)$

b)

$(5v+8)(v-8)$

c)

$(5v+32)(v-2)$

d)

$5(v-8)^2$

76.

Factor:

$5a^2-48a+27$

a)

$(5a+27)(a+1)$

b)

$(5a+3)(a+9)$

c)

$(5a-3)(a-9)$

d)

$(2a-9)(a+6)$

77.

Factor:

2p^2+p-45

a)

Not factorable

b)

$(2p+5)(p+2)$

c)

$(2p-9)(p+5)$

d)

$(2p+15)(p-3)$

78.

Factor:

$a^2+7a-8$

a)

$(a+1)(a+8)$

b)

$(a+1)(a-8)$

c)

$(a-1)(a-8)$

d)

$(a-1)(a+8)$

79.

Factor:

$6k^3+36k^2-96k$

a)

$6(k-2)(k-8)$

b)

$-3k(k+2)(k-5)$

c)

$6k(k-2)(k-8)$

d)

$6k(k-2)(k+8)$

80.

Factor:

$3k^2-28k+60$

a)

$3(k-10)(k+6)$

b)

$3(k-10)(k+2)$

c)

$(3k-10)(k-6)$

d)

$(3k+10)(k+6)$

81.

Solve by factoring: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

82.

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

83.

Solve for the values of x:
(x + 2)(x - 3) = 0

a)

{ 2, 3 }

b)

{ -2, -3 }

c)

{ 2, 3 }

d)

{ -2, 3 }

84.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Find two numbers which add to make 6 and multiply to make -13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

85.

Solve using Zero-Product Property.

(2x - 2)(5x + 5) = 0

a)

x = -1

b)

x = -1 or x = 1

c)

x = 1

d)

x = -2 or x = 5

86.

Convert x²-6x+9 to factored form and identify the solution.

a)

(x-3)(x-3); x=3

b)

(x+3)(x+3); x=-3

c)

(x+4)(x+2); x=-4, -2

d)

Not factorable

87.

Solve the following quadratic...

x² + 5x + 6 = 0

a)

x = -2, -3

b)

x = 1, 6

c)

x = -1, -6

d)

x = 2, 3

88.

Solve the following quadratic...

x² + 12x + 20 = 0

a)

x = 5, 4

b)

x = 2, 10

c)

x = -5, -4

d)

x = -2, -10

89.

Solve the following quadratic...

x² + 5x - 24 = 0

a)

x = 3, 8

b)

x = -3, -8

c)

x = -3, 8

d)

x = 3, -8

90.

What is the standard form for a Quadratic?

a)

ax²+ bx = - c

b)

x = -b ± √(b²-4ac) / 2a

c)

ax² + bx + c

d)

y = mx + b

91.

Solve by factoring: 2x² - 5x - 12 = 0

a)

x = -4 and x = -6

b)

x = 4 and x = -3/2

c)

x = 4 and x = 6

d)

x = -4 and x = 3/2

92.

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

93.

Solve by factoring: 4x² + 11x - 3 = 0

a)

x = -3/4 and x = -1

b)

x = 4 and x = 3

c)

x = 1/4 and x = -3

d)

x = -1/4 and x = 3

94.

Solve by factoring:3x² + 5x + 2 = 0

a)

x = -2/3 and x = -1

b)

x = -3/2 and x = -1

c)

x = 2/3 and x = 1

d)

x = 2/3 and x = -1

95.

Solve by factoring: 2x²+ 7x + 6 = 0

a)

x= 3/2 and x = 2

b)

x = -3/2 and x = -2

c)

x = 6 and x = 7

d)

x = -6 and x = -7

96.

Which of the following is a factor of: 6x²-5x-4

a)

(3x-4)

b)

(2x-1)

c)

(3x+4)

d)

(2x-3)

97.

The solutions of the quadratic equation
x²+2x-15=0 are

a)

x = 3 or x = 5

b)

x = 5 or x = -3

c)

x = -5 or x = 3

d)

x = -3 or x = -5

98.

The solutions of the quadratic equation
x²+12x+35=0 are

a)

x = -5 or x = -7

b)

x = 5 or x = 7

c)

x = -35 or x = -1

d)

x = -9 or x = -4

99.

Solve by factoring:
2x² + 11x - 6 = 0

a)

1/2 and -6

b)

6 and -1/2

c)

2 and -6

d)

11

100.

Solve the following equation using the quadratic formula:
2x² - 5x - 7 = 0

a)

{-7/2, 1}

b)

{7/2, -1}

c)

{-7/2, -1}

d)

{3, -1}

101.

24k²+24k=0

a)

k=1 and k=24

b)

k=-1 and k=24

c)

k=0 and k=1

d)

k=0 and k=-1

102.

-10b²+25b=0

a)

b=-5 and b=2.5

b)

b=-10 and b=5

c)

b=0 and b=2.5

d)

b=5 an b=-2.5

103.

Solve by factoring.
z² - 6z - 27 = 0

a)

z = 3 or z = 9

b)

z = 3 or z = -9

c)

z = -3 or z = 9

d)

z = -3 or z = -9

104.

Solve by factoring.
b² + 2b - 24 = 0

a)

x = 6 or x = -4

b)

x = -6 or x = -4

c)

x = 6 or x = 4

d)

x = -6 or x = 4

105.

Solve by factoring.
b² + 2b - 24 = 0

a)

x = 6 or x = -4

b)

x = -6 or x = -4

c)

x = 6 or x = 4

d)

x = -6 or x = 4

106.

Solve each equation by factoring.

$v^2-6v=-8$

(a)

107.

Solve each equation by factoring.

$r^2-9r+18=0$

(a)

108.

Solve by Factoring:

x² + 15x = - 44

a)

{-8, 2}

b)

{-7, 5}

c)

{-11, -4}

d)

{-11}

109.

Solve by factoring: x² = 7x + 18

a)

-7 and -18

b)

9 and 2

c)

9 and -2

d)

2 and 7

110.

Solve the equation by factoring.

a)

x = {-5,-3}

b)

x = {5,-3}

c)

x = {-5,3}

d)

x = {5,3}

111.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Find two numbers which add to make 6 and multiply to make -13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

112.

ax²+bx+c=0 is the standard form of a quadratic equation.

a)

True

b)

False

113.

Solve the following quadratic equation...

x² + 13x + 36= 0

a)

x = -2

x = -18

b)

x = -9

x = -4

c)

x = -3

x = -12

d)

x = -6

114.

Solve by factoring: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

115.

Which answer choice correctly shows the quadratic equation above in factored form?

a)

(x + 7)(x - 2) = 0

b)

(x - 7)(x + 2) = 0

c)

(x - 7)(x - 2) = 0

d)

(x + 7)(x + 2) = 0

116.

Solve the equation by factoring:

x²-6x+8=0

a)

x = 2 or x = 4

b)

x = -2 or x = -4

c)

x = -2 or x = 4

d)

x = 2 or x = -4

117.

True or false:
The solutions, roots, x-intercepts, and zeros of a quadratic equation are all the same thing.

a)

True

b)

False, because the solution and root are the same but the x-intercept and zero are different

c)

False, because the x-intercept and root are the same but the zero and solution are different

d)

False, they are all different

118.

What is another word for zeros?

a)

y-intercepts

b)

roots

c)

vertex

d)

axis of symmetry

Alg2 - Test 6 - Factoring Quadratic Expressions and Equations

Total questions: 118

Worksheet time: 8hrs 22mins

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