Free Printable Factoring Quadratic Expressions Test

1.

$x^2+7x+12$

a)

(x + 3)(x + 4)

b)

(x + 6)(x + 2)

c)

(x - 3)(x - 4)

d)

(x + 1)(x + 12)

2.

$x^2+6x-27$

a)

(x - 9)(x + 3)

b)

(x + 9)(x - 3)

c)

(x + 3)(x + 3)

d)

(x + 9)(x + 3)

3.

$2x^2-15x+7$

a)

(2x + 1)(x - 7)

b)

(2x + 7)(x - 1)

c)

(2x + 1)(x + 7)

d)

(2x - 1)(x - 7)

4.

$5x^2-13x-6$

a)

(5x + 2)(x - 3)

b)

(5x - 2)(x + 3)

c)

(5x + 1)(x - 6)

d)

(x + 3)(5x + 2)

5.

$3x^2+22x-16$

a)

(3x + 2)(x + 8)

b)

(3x - 2)(x + 8)

c)

(3x - 4)(x + 4)

d)

(3x - 2)(x - 8)

6.

$x^2-\ 7x\ -18$

a)

(x + 9)(x + 2)

b)

(x - 9)(x - 2)

c)

(x - 9)(x + 2)

d)

(x + 9)(x - 2)

7.

$6x^2+11x+4$

a)

(6x + 1)(x + 4)

b)

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

c)

(6x + 2)(x + 2)

d)

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

8.

$x^2-20x+64$

a)

(x - 4)(x - 16)

b)

(x + 4)(x + 16)

c)

(x - 8)(x - 8)

d)

(x + 32)(x - 2)

9.

$x^2+12x-45$

a)

(x - 15)(x + 3)

b)

(x - 15)(x - 3)

c)

(x + 9)(x - 5)

d)

(x + 15)(x - 3)

10.

$4x^2-21x-18$

a)

(4x - 3)(x + 6)

b)

(2x + 9)(2x - 2)

c)

(4x + 3)(x - 6)

d)

(2x - 3)(2x + 6)

11.

$9x^2-6x-8$

a)

(3x - 4)(3x - 2)

b)

(3x + 2)(3x + 4)

c)

(3x + 8)(3x - 1)

d)

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

12.

$8x^2-22x+5$

a)

(8x - 5)(x + 1)

b)

(4x - 1)(2x - 5)

c)

(4x + 5)(2x + 1)

d)

(8x - 1)(x - 1)

13.

x² − 7x − 18

a)

(x − 9)(x + 2)

b)

(x + 9)(x + 2)

c)

(x − 9)(x - 2)

d)

(x − 9)(x - 2)

14.

p² − 5p − 14

a)

( p + 2)( p + 7)

b)

( p + 2)( p − 7)

c)

( p - 2)( p − 7)

d)

( p - 2)( p + 7)

15.

m² − 9m + 8

a)

(m + 1)(m − 8)

b)

(m − 1)(m + 8)

c)

(m − 1)(m − 8)

d)

(m + 1)(m + 8)

16.

x² − 16x + 63

a)

(x + 9)(x + 7)

b)

(x − 9)(x + 7)

c)

(x + 9)(x − 7)

d)

(x − 9)(x − 7)

17.

7x² − 31x − 20

a)

(7x + 4)(x − 5)

b)

(7x - 4)(x − 5)

c)

(7x + 4)(x + 5)

d)

(7x - 4)(x − 5)

18.

7k² + 9k

a)

k(7k - 9)

b)

k(7k + 9)

c)

7k(k + 9)

d)

(k+3)(7k + 3)

19.

7x² − 45x − 28

a)

7(x + 4)(x − 7)

b)

(x + 4)(7x - 7)

c)

(7x + 4)(x − 7)

d)

(7x - 4)(x + 7)

20.

2b² + 17b + 21

a)

(2b + 7)(b + 3)

b)

(2b + 3)(b - 7)

c)

2(b + 3)(b + 7)

d)

(2b + 3)(b + 7)

21.

5p² − p − 18

a)

5(p + 9)( p − 2)

b)

(p + 9)( 5p − 2)

c)

(5p - 9)( p + 2)

d)

(5p + 9)( p − 2)

22.

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)

23.

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)

24.

7x² − 32x − 60

a)

(7x + 10)(x − 6)

b)

7(x + 10)(x − 6)

c)

(7x - 10)(x − 6)

d)

(7x - 10)(x + 6)

25.

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)

26.

9r² − 5r − 10

a)

(9r + 2)(r - 5)

b)

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

c)

9(r + 2)(r - 5)

d)

not factorable

27.

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)

28.

9x² + 7x − 56

a)

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

b)

9(x + 7)(x - 8)

c)

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

d)

not factorable

29.

10m² + 89m − 9

a)

(m + 9)(10m + 1)

b)

(m + 9)(10m − 1)

c)

(m - 9)(10m − 1)

d)

not factorable

30.

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)

31.

Factor: $7k^2+9k$

a)

$k\left(7+9\right)$

b)

$7k\left(k+9\right)$

c)

$k\left(7k+9\right)$

d)

$k^{2\left(7+9\right)}$

32.

Factor $p^2-5p-14$

a)

$\left(p+7\right)\left(p-2\right)$

b)

$\left(p+2\right)\left(p-7\right)$

33.

Factor $m^2-9m+8$

a)

$\left(m-1\right)\left(m-8\right)$

b)

$\left(m+8\right)\left(m-1\right)$

34.

Factor $2b^2+17b+21$

a)

$\left(2b+7\right)\left(b-3\right)$

b)

$\left(b-7\right)\left(2b-3\right)$

c)

$\left(2b+3\right)\left(b+7\right)$

d)

$\left(2b-7\right)\left(b-3\right)$

35.

Factor $28n^4+16n^3-80n^2$

a)

$4n^2\left(7n^2+4n-20\right)$

b)

$\left(7n-10\right)\left(n+2\right)$

c)

$\left(28n^3-40n^2\right)\left(n+2\right)$

d)

$4n^2\left(7n-10\right)\left(n+2\right)$

36.

Factor $5p^2-p-18$

a)

$\left(5p-9\right)\left(p+2\right)$

b)

$\left(5p+9\right)\left(p-2\right)$

c)

$\left(p+9\right)\left(9p-5\right)$

d)

$\left(9p+5\right)\left(2p-1\right)$

37.

Factor:

x² + 11x + 24

a)

(x + 6)(x + 4)

b)

(x + 12)(x + 2)

c)

(x - 8)(x - 3)

d)

(x + 8)(x + 3)

38.

What are the factors of x²+3x-40

a)

(x+10)(x-4)

b)

(x+8)(x-5)

c)

(x+20)(x-2)

d)

(x+1)(x-3)

39.

Find the factors of 5x²+20x+20

a)

5(x+2)(x+2)

b)

5(x-2)(x-2)

c)

5(x+2)(x-2)

d)

(5x+2)(x+2)

40.

Factor:

5x³- 7x²

a)

x²(5x - 7)

b)

x(5x²- 7x)

c)

x³(5 - 7x)

d)

Prime

41.

Factor: 25x²- 9

a)

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

b)

(x + 5)(x - 3)

c)

(x - 3)(x + 5)

d)

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

42.

Factor d² - 10d + 25

a)

(d + 5) (d - 5)

b)

(d - 15) (d + 10)

c)

(d + 5) (d - 20)

d)

(d - 5) (d - 5)

43.

x² − 7x − 18

a)

(x − 9)(x + 2)

b)

(x + 9)(x + 2)

c)

(x − 9)(x - 2)

d)

(x − 9)(x - 2)

44.

p² − 5p − 14

a)

( p + 2)( p + 7)

b)

( p + 2)( p − 7)

c)

( p - 2)( p − 7)

d)

( p - 2)( p + 7)

45.

m² − 9m + 8

a)

(m + 1)(m − 8)

b)

(m − 1)(m + 8)

c)

(m − 1)(m − 8)

d)

(m + 1)(m + 8)

46.

x² − 16x + 63

a)

(x + 9)(x + 7)

b)

(x − 9)(x + 7)

c)

(x + 9)(x − 7)

d)

(x − 9)(x − 7)

47.

2b² + 17b + 21

a)

(2b + 7)(b + 3)

b)

(2b + 3)(b - 7)

c)

2(b + 3)(b + 7)

d)

(2b + 3)(b + 7)

48.

5p² − p − 18

a)

5(p + 9)( p − 2)

b)

(p + 9)( 5p − 2)

c)

(5p - 9)( p + 2)

d)

(5p + 9)( p − 2)

49.

10m² + 89m − 9

a)

(m + 9)(10m + 1)

b)

(m + 9)(10m − 1)

c)

(m - 9)(10m − 1)

d)

not factorable

50.

Factor completely.
$x^2-16$

a)

(x + 8)(x - 8)

b)

(x + 4)(x - 4)

c)

(x + 6)(x - 10)

d)

(x + 4)(x + 4)

51.

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

52.

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

53.

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

a)

{ 2, 3 }

b)

{ -2, -3 }

c)

{ 2, 3 }

d)

{ -2, 3 }

54.

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.

55.

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

56.

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

57.

Solve the following quadratic...

x² + 5x + 6 = 0

a)

x = -2, -3

b)

x = 1, 6

c)

x = -1, -6

d)

x = 2, 3

58.

Solve the following quadratic...

x² + 12x + 20 = 0

a)

x = 5, 4

b)

x = 2, 10

c)

x = -5, -4

d)

x = -2, -10

59.

Solve the following quadratic...

x² + 5x - 24 = 0

a)

x = 3, 8

b)

x = -3, -8

c)

x = -3, 8

d)

x = 3, -8

60.

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

61.

Solve by completing the square.
x² + 4x= 12

a)

x = 2 and -2

b)

x = -6 and 2

c)

x = 6 and -2

d)

x = 1 and -1

62.

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

a)

True

b)

False

63.

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

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

64.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

65.

Factor x²-11x+24

a)

(x-3)(x-8)

b)

(x-2)(x-12)

c)

(x+3)(x+8)

d)

(x+2)(x+12)

66.

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

a)

{ 2, 3 }

b)

{ -2, -3 }

c)

{ 2, 3 }

d)

{ -2, 3 }

67.

Solve by factoring

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

68.

Solve using the Quadratic Formula:

2x² + 2x − 12 = 0

a)

x = −2, 3

b)

x = 2, 3

c)

x = 2, −3

d)

x = −2, −3

69.

Solve by factoring. (HINT: Factor GCF 1st)

a)

x = 3, x = -6

b)

x = 0, x = 2

c)

x = 2, x = 3

d)

x = -2, x = 1

70.

What number added would make a perfect square trinomial?

x² - 8x + ______

a)

-4

b)

-64

c)

12

d)

16

71.

Factor Completely:
3x² + 18x +15

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

72.

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)

73.

Solve the following quadratic equation...

x² + 3x + 2 = 0

a)

x = -1

x = -2

b)

x = 1

x = 2

c)

x = -1

x = 2

d)

x = 1

x = -2

74.

Solve the following quadratic equation...

x² + 7x + 12 = 0

a)

x = -2

x = -6

b)

x = -3

x = -4

c)

x = -1

x = -12

d)

x = 2

x = 6

75.

Solve the following quadratic equation...

x² + 9x + 20 = 0

a)

x = -2

x = -10

b)

x = -5

x = -4

c)

x = -1

x = -20

d)

x = 4

x = 5

76.

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

77.

Solve the following quadratic equation...

x² + 4x - 32 = 0

a)

x = 8

x = -4

b)

x = -8

x = 4

c)

x = -2

x = 16

d)

x = 2

x = -16

78.

Solve the following quadratic equation...

x² - 2x - 15 = 0

a)

x = 5

x = -3

b)

x = -5

x = 3

c)

x = -15

x = 1

d)

x = 15

x = -1

79.

Solve the following quadratic equation...

x² - 13x + 30 = 0

a)

x = 10

x = 3

b)

x = -10

x = -3

c)

x = 5

x = 6

d)

x = -5

x = -6

80.

Solve the following quadratic equation...

x² - 14x + 24 = 0

a)

x = 12

x = 2

b)

x = 4

x = 6

c)

x = 3

x = 8

d)

x = 1

x = 24

81.

Solve the following quadratic...

x² + 5x + 6 = 0

a)

x = -2, -3

b)

x = 1, 6

c)

x = -1, -6

d)

x = 2, 3

82.

Solve the following quadratic...

x² + 7x + 12 = 0

a)

x = 3, 4

b)

x = 2, 6

c)

x = -3, -4

d)

x = -2, -6

83.

Solve the following quadratic...

x² + 12x + 20 = 0

a)

x = 5, 4

b)

x = 2, 10

c)

x = -5, -4

d)

x = -2, -10

84.

Solve the following quadratic...

x² + 11x + 24 = 0

a)

x = -3, -8

b)

x = 2, 12

c)

x = -4, -6

d)

x = -2, -12

85.

Solve the following quadratic...

x² + 11x + 30 = 0

a)

x = -5, 6

b)

x = -5, -6

c)

x = 5, -6

d)

x = 5, 6

86.

Solve the following quadratic...

x² + 8x + 15 = 0

a)

x = -3, 5

b)

x = 3, -5

c)

x = 3, 5

d)

x = -3, -5

87.

Solve the following quadratic...

x² + x - 20 = 0

a)

x = -4, 5

b)

x = 4, -5

c)

x = 4, 5

d)

x = -4, -5

88.

Solve the following quadratic...

x² + 5x - 24 = 0

a)

x = 3, 8

b)

x = -3, -8

c)

x = -3, 8

d)

x = 3, -8

89.

Solve the following quadratic...

x² - 7x - 30 = 0

a)

x = 3, 10

b)

x = -3, -10

c)

x = -3, 10

d)

x = 3, -10

90.

Solve the following quadratic...

x² - 7x + 12 = 0

a)

x = 3, 4

b)

x = -3, -4

c)

x = -2, -6

d)

x = 2, 6

91.

x² + 5x + 6, What two numbers multiply together to give 6 but when added together give 5 ?

a)

1 and 4

b)

1 and 6

c)

2 and 3

d)

0 and 5

92.

x² + 7x + 10, What two numbers multiply together to give 10 but when added together give 7 ?

a)

3 and 4

b)

2 and 5

c)

1 and 10

d)

6 sand 1

93.

x² + 4x - 5, What two numbers multiply together to give -5 but when added together give 4 ?

a)

2 and 2

b)

-5 and 1

c)

1 and 5

d)

-1 and 5

94.

x² + 4x - 21, What two numbers multiply together to give -21 but when added together give 4 ?

a)

-1 and 21

b)

-3 and 7

c)

-7 and -3

d)

-7 and 3

95.

x² + 2x - 15, What two numbers multiply together to give -15 but when added together give 2 ?

a)

-3 and 5

b)

3 and -5

c)

-1 and 15

d)

-15 and 1

96.

x² - 5x + 6, What two numbers multiply together to give 6 but when added together give -5 ?

a)

-1 and -4

b)

1 and 6

c)

-2 and -3

d)

2 and 3

97.

x² - 9x + 14, What two numbers multiply together to give 14 but when added together give -9 ?

a)

-9 and 1

b)

1 and -9

c)

-2 and -7

d)

2 and 7

98.

Factorise x² + 5x + 6

a)

(x+2)(x+3)

b)

(x+1)(x+6)

c)

(x+1)(x+5)

d)

(x-1)(x+6)

99.

Factorise x² + 4x - 21

a)

(x-2)(x+2)

b)

(x-1)(x+21)

c)

(x-3)(x+7)

d)

(x+3)(x+7)

100.

Factorise x² - 5x +6

a)

(x-1)(x-5)

b)

(x-2)(x-3)

c)

(x+2)(x-3)

d)

(x+2)(x+3)

Factoring Quadratic Expressions Test

Total questions: 100

Worksheet time: 3hrs 24mins

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