Free Printable Linear and Quadratic Equations

1.

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)

2.

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)

3.

Factor completely: x²-13x+40

a)

(x-5)(x-8)

b)

(x+5)(x+8)

c)

(x-4)(x-10)

d)

(x-2)(x-20)

4.

Factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

5.

Factor out the GCF:
12x + 6

a)

6(2x + 1)

b)

3(4x + 2)

c)

6x(2x + 1)

d)

2(6x + 3)

6.

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

7.

Factor out the GCF:
10x³ - 15x

a)

x(10x² - 15)

b)

5x(2x² - 3)

c)

5(2x³ - 3x)

d)

5x²(10x - 3)

8.

Factor:
4x² + 64

a)

4(x² + 16)

b)

4(x - 4)(x + 4)

c)

4(x²+ 64)

d)

Prime

9.

Factor: 24x + 18

a)

2(12X + 9)

b)

3(8x + 6)

c)

1(24x + 18)

d)

6(4x + 3)

10.

Factor by using GCF:
8n³ + 2n²

a)

2n²(4n - 1)

b)

2n²(4n + 1)

c)

n²(8n + 2)

d)

3n(4n + 1)

11.

Factor:
10x + 15

a)

100x + 150

b)

10(x + 5)

c)

1(10x + 15)

d)

5(2x + 3)

12.

Factor
-8x - 10

a)

4(2x - 3)

b)

-2(4x + 5)

c)

-2(4x - 5)

d)

4(2x + 3)

13.

Factor:
7x + 48y

a)

7(x + 7y)

b)

7(x + y)

c)

can't be factored

d)

7(x + 48y)

14.

Factor completely: 16 + 24x

a)

8 ( 2 + 3x)

b)

4 ( 4 + 7x)

c)

8 ( 2 - 3x)

d)

6 ( 4x + 3)

15.

Factor 12x - 20

a)

6(2x - 3)

b)

4(3x - 5)

c)

4x(3x - 5)

d)

3(4x + 6)

16.

Factor Completely:
24+16q

a)

4(7+4q)

b)

8(3+2q)

c)

4(6q+2)

d)

24(24-16q)

17.

10x + 50

a)

10(10x+50)

b)

10(x+50)

c)

10(x+5)

d)

Cannot be factored

18.

-6y + 36

a)

-6 (y -6)

b)

6 (y + 6)

c)

-6 (1)

d)

cannot be factored

19.

9x + 3

a)

9 (x+1)

b)

3( 3x +1)

c)

3(3x + 3)

d)

cannot be factored

20.

Factor by GCF:
17xy - x

a)

17(xy - x)

b)

y(17x - x)

c)

x(17y - 1)

d)

not factorable

21.

Solve the following equation,
x + 7 = 28

a)

x = 35

b)

x = 4

c)

x = 196

d)

x = 21

22.

Solve the following equation,
x - 23 = 17

a)

-6

b)

6

c)

40

d)

-40

23.

Solve the following equation,
5x = 30

a)

x = 6

b)

x = 150

c)

x = -6

d)

x = -150

24.

Solve the following equation,
3x + 6 = 21

a)

x = 9

b)

x = 5

c)

x = 15

d)

x = 27

25.

Solve the following equation,
7x - 9 = 33

a)

x = 24/7

b)

x = 42

c)

x = 24

d)

x = 6

26.

Expand the following,
3(x - 5)

a)

3x - 5

b)

-15x

c)

3x - 15

d)

-2x

27.

2x(5x - 3)

a)

10x - 6x

b)

10x² - 6x

c)

7x² - 6x

d)

4x

28.

3(5x + 1) = 48

a)

x = 47/15

b)

x = 47

c)

x = 51

d)

x = 3

29.

5(2x - 7) = 80

a)

x = 11.5

b)

x = 115

c)

x = 12

d)

x = 16

30.

Solve the following equation,

5x = -30

a)

x = 6

b)

x = 150

c)

x = -6

d)

x = -150

31.

In the equation 3x + 8=23, the number 3 is called the ____________.

a)

variable

b)

constant

c)

coefficient

d)

answer

32.

In the equation 2x-5=27, which of the following is the variable?

a)

2

b)

x

c)

-5

d)

27

33.

What is the value of a in the equation 3a-7=17?

a)

a = 6

b)

a = 8

c)

a = -8

d)

a = $\frac{10}{3}$

34.

Solve:
7x - 3x - 8 = 24

a)

8

b)

-8

c)

3.2

d)

4

35.

Solve:
3(x - 2) = 18

a)

6.7

b)

4

c)

8

d)

-4

36.

Solve:
7x + 19 = -2x + 55

a)

4

b)

14.8

c)

8.2

d)

-4

37.

Solve:
2(2x + 3) = -6(x + 9)

a)

1.2

b)

6

c)

-6

d)

7.5

38.

Solve for x:
4x + 1 = 7x - 5

a)

-1

b)

2

c)

6/11

d)

8

39.

Solve for x:
6(2x + 1) = 18

a)

3

b)

17/12

c)

1

d)

2

40.

Solve for x:
5 + 3x = 8x - 15

a)

10

b)

4

c)

2

d)

20/11

41.

Solve

-5x + 1 = -19

a)

x=4

b)

x=-4

c)

x=5

d)

x=-5

42.

Solve

5x+3=4x-10

a)

x=13

b)

x=-13

c)

x=16

d)

x=3

43.

Solve

-3x - 9 = 2x +1

a)

x=-2

b)

x=2

c)

x=5

d)

x=-5

44.

Solve

-3(2x-1)=15

a)

x=6

b)

x=-6

c)

x=2

d)

x=-2

45.

Solve

-20 = 5(x+2)

a)

x=4

b)

x=-4

c)

x=-6

d)

x=6

46.

Multiply: (v - 1)(3v - 1)

a)

2v²-2

b)

2v² + 2v -2

c)

3v²+ 4v - 1

d)

3v²- 4v + 1

47.

Multiply: (6x + 2)(2x + 8)

a)

8x² + 48x + 16

b)

12x² + 18x + 10

c)

8x² + 18x + 10

d)

12x²+ 52x + 16

48.

$\left(a-5\right)\left(a+2\right)=$

a)

$a^2-3a-10$

b)

$2a^2+7a-10$

c)

$a^2+3a+10$

d)

$2a^2+9a+7$

49.

$\left(2x-3\right)\left(x+6\right)=$

a)

$2x^2-15x-9$

b)

$2x^2+15x+18$

c)

$2x^2+9x-18$

d)

$2x^2+9x-9$

50.

$\left(3x+1\right)\left(4x+2\right)=$

a)

$7x^2+10x+2$

b)

$12x^2+10x+2$

c)

$7x^2-10x-2$

d)

$12x^2+24x+3$

51.

$\left(y+4\right)^2=$

a)

$y^2+16$

b)

$y^2+8y+16$

c)

$2y+8$

d)

$y^2+16y+8$

52.

Multiply:

(3y - 4)(2y + 5)

a)

5y² - 20

b)

6y² + y - 20

c)

6y² + 11y - 20

d)

6y² + 7y - 20

53.

(d + 3)²

a)

d² + 6d + 9

b)

d² + 9d + 9

c)

d² + 6d + 6

d)

d² + 9

54.

(x - 4)²

a)

x² + 8x - 16

b)

x² - 8x + 16

c)

x² - 16x + 8

d)

x² + 16

55.

(y + 2)(y - 2)

a)

y² + 4

b)

y² + 4y - 4

c)

y² - 4y + 4

d)

y² - 4

56.

(c + 9)(c - 9)

a)

c² - 81

b)

c² + 81

c)

c² - 18c - 81

d)

c² + 18c - 81

57.

Multiply:
(3x – 1)(x + 5)

a)

3x² + 4x + 5

b)

3x² + 4x - 5

c)

3x² + 14x + 5

d)

3x² + 14x - 5

58.

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

a)

6x² + 16x + 8

b)

5x² +11x + 6

c)

5x² + 16x + 6

d)

6x² + 11x + 8

59.

Find the product:
(x + 5)(x - 4)

a)

x² + 9x + 20

b)

x² + 9x - 20

c)

x² + 1x - 20

d)

x² - 1x - 20

60.

Simplify:
(x - 7)(x + 7)

a)

x² + 7x - 49

b)

x² - 7x + 49

c)

x² - 49

d)

x² + 49

61.

Simplify
(p − 8)²
Hint: (p − 8)² = (p − 8)(p − 8)

a)

p ² − 16p − 64

b)

p ² + 16p + 64

c)

p ² − 16p − 8

d)

p ² − 16p + 64

62.

Simplify:
(x-7)²

a)

x²-49

b)

x²+49

c)

x²-14x+49

d)

x²-14x-49

63.

Find the product:
(x + 12)(x - 12)

a)

x² - 144

b)

x² + 144

c)

x² + 12x - 144

d)

x² - 12x + 144

64.

(2x + 8)(5x + 1)

a)

7x² + 2x + 9

b)

10x² + 42x + 8

c)

7x² + 42x + 8

d)

10x² + 40x + 8

65.

(r - 7)(2r + 8)

a)

2r² - 7r - 55

b)

2r² - 6r - 56

c)

2r² - 123 - 56

d)

bananas

66.

5(2 - 7n)

a)

52 - 57n

b)

10 - 7n

c)

10 - 35n

d)

10 + 35n

67.

6(x + -2)

a)

6x + -2

b)

6x + -12

c)

4x

d)

6x - 2

68.

6 + 2(7x - 3)

a)

12 + 7x

b)

14x

c)

14x + 3

d)

9 + 7x

69.

6w - 6w + 6w + 9w

a)

w

b)

15w

c)

9w

d)

6w

70.

4a + 9 + a

a)

5a + 9

b)

14a

c)

3a + 9

d)

5a - 9

71.

9z - 21 - 3z + 10

a)

Simplified

b)

9z - 21 - 7

c)

9z - 11 -3z

d)

6z - 11

72.

5x - 6x - 8x + 7

a)

-9x + 7

b)

10x + 7

c)

9x + 7

d)

9x - 7

73.

7+3(1 - 2x)

a)

21 - 6x

b)

10 - 2x

c)

10 - 20x

d)

10 - 6x

74.

2x + 1 + 7x

a)

10x

b)

10

c)

9x + 1

d)

9 + 1x

75.

7v + 2 + 12 + 2v

a)

23

b)

23v

c)

9 + 14v

d)

9v + 14

76.

7d + 5 + 6d - 2

a)

16d

b)

16

c)

13d + 3

d)

13d - 7

77.

5a + 2b + 6a + 4b

a)

11a + 6b

b)

2a + 2b

c)

a + 2b

d)

-a - 2b

78.

15x-2x+12

a)

-13x+12

b)

12x+13x

c)

13-12+x

d)

13x+12

79.

4(x + 2) + 6x

a)

4x + 2 + 6x

b)

4x + 8 + 6x

c)

10x + 8

d)

10x + 2

80.

8x - 2(x + 3)

a)

6x - 6

b)

6x - 5

c)

6x + 6

d)

6x + 3

Linear and Quadratic Equations

Total questions: 80

Worksheet time: 5hrs 17mins

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