Free Printable Lessons 4-5 and 4-6

1.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

2.

To solve by completing the square, what needs to be moved in this equation?
x² = 9 - 4x

a)

the -4x

b)

the 9

c)

the x²

3.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

4.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

5.

When do you use the plus or minus symbol?
±

a)

After taking the square root of both sides

b)

After adding the square to both sides

c)

After taking half of b

d)

After setting the equation equal to zero

6.

Solve the following equation by completing the square:
n² - 2n - 3 = 0

a)

{3, -1}

b)

{4, -4}

c)

{5, -3}

d)

{8, -7}

7.

Solve the following equation by completing the square:
n² = 18n + 40

a)

{11, -11}

b)

{16, 2}

c)

{20, -2}

d)

{10, -4}

8.

Solve by completing the square:
k² − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

9.

Factor the perfect square trinomial:
x² + 16x + 64

a)

(x+8)²

b)

(x-8)²

c)

(x-4)²

d)

(x+4)²

10.

Factor the perfect square trinomial
x² + 14x + 49

a)

(x+7)²

b)

(x+7)(x-7)

c)

(x-7)²

d)

(x+14)²

11.

Factor the perfect square trinomial
x² - 6x + 9

a)

(x-3)²

b)

(x+3)²

c)

(x+3)(x-3)

d)

(x+9)²

12.

Is this a perfect square trinomial? If so, factor it!

x² - 20x + 100

a)

$\left(x+10\right)^2$ Yes

b)

$\left(x-10\right)^2$

c)

No!

d)

$\left(x+10\right)\left(x-10\right)$

13.

What value of c would make this a perfect sqaure trinomial?
x² +8x + c

a)

4

b)

16

c)

64

d)

-16

14.

What value of c would make this a perfect square trinomial?
x² + 2x + c

a)

2

b)

4

c)

-2

d)

1

15.

What value of c would make this a perfect square trinomial?
x²- 12x + c

a)

36

b)

24

c)

144

d)

-36

16.

Factor: x² - 4x + 4

a)

(x + 2)²

b)

(x - 2)²

c)

(x + 4)²

d)

(x - 4)²

17.

Factor: x² - 30x + 225

a)

(x + 15)²

b)

(x - 15)²

c)

(x + 25)²

d)

(x - 25)²

18.

Find the missing value "c" to create a perfect square trinomial:
x² + 26x + ___

a)

13

b)

136

c)

169

d)

26

19.

Find the missing value "c" to create a perfect square trinomial:
x² – 8x + ___

a)

-4

b)

16

c)

4

d)

8

20.

Factor the following perfect square trinomial using the rule(b/2)² :

x² – 12x + 36

a)

(x – 6)(x – 6)

b)

(x – 6)²

c)

(x – 6)(x + 6)

d)

(x + 6)²

21.

Factor the following perfect square trinomial using the rule(b/2)² :

x² + 18x + 81

a)

(x + 9)(x – 9)

b)

(x + 18)²

c)

(x + 9)²

d)

(x + 6)²

22.

Find the missing c of
x²+ 18x + c

a)

100

b)

18

c)

72

d)

81

23.

Find the missing c of
x²+ 40x + c

a)

20

b)

200

c)

40

d)

400

24.

Complete the Square and solve the equation.
r² - 4r = 30

a)

2 ± √ 34

b)

± √ 34

c)

34

d)

± 2

25.

Complete the Square and solve the equation.
m² - 16m = -59

a)

8

b)

8 ± √ 5

c)

± √ 13

d)

-8 ± √ 5

26.

Complete the Square and solve the equation.
a² - 2a - 35 = 0

a)

1 ± √ 6

b)

-7, 7

c)

-5, 7

d)

35, 37

27.

Complete the Square and solve the equation.
m² + 12m + 19 = 0

a)

- 6 ± √ - 19

b)

6 ± √ 19

c)

- 23, - 11

d)

- 6 ± √ 17

28.

Solve the equation by completing the square and then finding the roots.
x²+ 6x - 4 = 36

a)

x = -7, 7

b)

x = 4, -10

c)

x = -4 +- √7

d)

x = 10, -4

29.

Solve the following equation by completing the square:
n² - 2n - 3 = 0

a)

{3 and-1}

b)

{4 and -4}

c)

{5 and -3}

d)

{8 and -7}

30.

Solve by completing the square.
y² + 10y = -9

a)

1 and -12

b)

-1 and -9

c)

1 and -9

d)

1 and -1

31.

Solve by completing the square.
$x^2+12x=5$

a)

X = 6 + √41 or 6 − √41

b)

X= 35 or 47

c)

X = −6 + √41 or −6 − √41

d)

X = √35 or √47

32.

Complete the square: Step 1 (May have more than one answer)

x²+ 6x - 40 = 0

a)

x²+ 6x = 40

b)

x²+ 6x = -40

c)

x²+ 6x + ___ = 40 + ___

d)

x²+ 6x + ___ = -40 + ___

33.

Complete the Square Step: Step 2
x²+ 6x + ___ = 40 + ___

a)

put 3 in the blanks/boxes

b)

put 6 in the blanks/boxes

c)

put 9 in the blanks/boxes

d)

What are the boxes for??

34.

Complete the Square Step: Step 3
x²+ 6x + 9 = 40 + 9

a)

(x + 3) (x - 3) = 49

b)

(x + 3)² = 31

c)

(x - 3)² = 49

d)

(x + 3)² = 49

35.

Complete the Square Step: Step 4 - Solving

(x - 3)² = 49

a)

x - 3 = 49

b)

x - 3 = ±7

c)

x - 3 = 24.5

d)

x - 3 = 7

36.

Complete the Square Step: Step 5 - Solving

x - 3 = ±7

a)

x = 10, -7

b)

x = 4, -10

c)

x = 10

d)

x = 4

37.

What do you need to add to complete the square? $x^2+6x+\ \ \ =20$

a)

9

b)

100

c)

36

d)

12

38.

Complete the square for the equation

x² + 26x = 0

a)

x² + 26x + 169 = 169

b)

x² + 26x + 13 = 13

c)

x² + 26x + 26 = 26

39.

Solve by completing the square. Round.
x² -4x = 5

a)

11 and -7

b)

1 and 3

c)

1.73 and -1.73

d)

5 and -1

40.

Solve by completing the square.
y² + 10y = -9

a)

1 and -12

b)

-1 and -9

c)

1 and -9

d)

1 and -1

41.

Solve the equation by completing the square and then finding the roots.
x²+ 6x - 4 = 36

a)

x = -7, 7

b)

x = 4, -10

c)

x = -4 +- √7

d)

x = 10, -4

42.

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

43.

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

44.

Solve for a by factoring.
a² + 2a - 24 = 0

a)

a = -6, 4

b)

a = 6, -4

c)

a = 12, -2

d)

a = 8, -3

45.

a² - 9a + 8 = 0

a)

{-4, 14}

b)

{-5, -4}

c)

{1, 8}

d)

{-4, 11}

46.

p² + 12p + 35 = 0

a)

{-7, 5}

b)

{-9, -5}

c)

{-7, 0}

d)

{-7, -5}

47.

n² - 15n + 56 = 0

a)

{3, 0}

b)

{-8, 8}

c)

{-3, 6}

d)

{7, 8}

48.

x² - 6x - 7 = 0

a)

{-1, 7}

b)

{-3, -1}

c)

{5, 6}

d)

{-3, 3}

49.

n² + 6n - 27 = 0

a)

{-3, 10}

b)

{5, 14}

c)

{-12, 4}

d)

{-9, 3}

50.

x² + 15x + 44 = 0

a)

{-8, 2}

b)

{-7, 5}

c)

{-11, -4}

d)

{-11}

51.

Solve for x by factoring. $x^2-8x+12=0$

a)

-6, -2

b)

-2, 6

c)

2, 6

d)

-6, 2

52.

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

53.

Solve the equation by factoring:
x²-6x+8=0

a)

2, 4

b)

-2, -4

c)

-2, 4

d)

2, -4

54.

3x²+9x-30=0

a)

x= 2, -5

b)

x= 5, -2

c)

x= -5, -2

55.

6x²-x-2=0

a)

x= -2/3, 1/2

b)

x= 2/3, -1/2

c)

x= -2/3, -1/2

56.

What are the zeros? (The same as the x-intercepts, solutions, or roots)

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

57.

Find the zeros. (The same as the x-intercepts, solutions, or roots)

a)

0 and 4

b)

0 and -4

c)

0

d)

-4

58.

What is the first step in solving
(x + 2)(x - 3) = 0 ?

a)

Plug in zero for x

b)

Solve for x

c)

FOIL

d)

Set each binomial factor equal to zero

59.

Which equation matches these solutions? x=5,-7

a)

(x+5)(x-7)=0

b)

(x-5)(x+7)=0

c)

(x+5)(x+7)=0

d)

(x-5)(x-7)=0

60.

Find the zeros of this quadratic. $\left(5b-4\right)\left(b+3\right)=0$

a)

b=4/5, b=3

b)

b=4, b=-3

c)

b=1/5, b=3

d)

b=4/5, b=-3

61.

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

a)

{ 2, 3 }

b)

{ -2, -3 }

c)

{ 2, 3 }

d)

{ -2, 3 }

62.

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

63.

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

64.

n² + 6n - 27 = 0

a)

{-3, 10}

b)

{5, 14}

c)

{-12, 4}

d)

{-9, 3}

65.

Solve
12x² - 2x = 80

a)

x = -30, 16

b)

x = 30, -16

c)

x = -8/3, 5/2

d)

x = 8/3, -5/2

66.

7x² - 26x - 8 = 0

a)

x = -1 and x = -7/8

b)

x = 4 and x = -2/7

c)

x = -4 and x = 2/7

d)

x = 4 and x = -7/2

67.

Solve: $2n^2+4n-16=0$

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

68.

Solve 2x² + 7x - 15 = 0

a)

-3/2 or 5

b)

No Solution

c)

-5 or 3/2

d)

7/10 or 5

69.

Solve the equation (7x+2)(5x-4)=0

a)

x=2 or -4

b)

x=2/7 or 4/5

c)

x=-2/7 , or 4/5

d)

x=-2, or 4

70.

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

71.

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

72.

Solve for the values of x:
(2x + 5)(5x - 2) = 0

a)

{ -5/2, -2/5 }

b)

{ -5/2, 2/5 }

c)

{ 5/2, 2/5 }

d)

{ 5/2, -2/5 }

73.

Solve using Zero-Product Property
(x - 11)(5x + 1) = 0

a)

x = 11 or x = -1/5

b)

x = -11 or x = -1/5

c)

x = 11 or x = 1/5

d)

x = -11 or x = 1/5

74.

Solve by factoring:

3x² - 11x + 6 = 0

a)

x = -2/3 and x = -3

b)

x = -1/3 and x = 6

c)

x = -3/2 and x = 3

d)

x = 2/3 and x = 3

75.

Solve by factoring:3x² + 5x + 2 = 0

a)

$x=-\frac{2}{3}\ and\ x=-1$

b)

$x=-\frac{3}{2}and\ x=-1$

c)

$x=\frac{2}{3}and\ x=1$

d)

$x=\frac{2}{3}and\ x=-1$

76.

Solve by factoring: 4x² + 11x - 3 = 0

a)

$x=-\frac{3}{4}$ and $x=-1$

b)

$x=4$ and $x=3$

c)

$x=\frac{1}{4}$ and $x=-3$

d)

$x=-\frac{1}{4}$ and $x=-3$

77.

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

78.

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

79.

What you do to one side of an equation you must...

a)

do to the other!

b)

do only to that side!

c)

divide and multiply!

d)

take the square root!

80.

In order to factor a quadratic equation, it must be equal to...

a)

a positive number

b)

a negative number

c)

zero

d)

a perfect square

81.

The solutions of a quadratic equation are the same as its...

a)

x-intercepts

b)

zeroes

c)

roots

d)

All the Above!

82.

If the b term is 16x, what is the new c term?

a)

16

b)

64

c)

8

d)

24

83.

If the b term is 20x, what is the new c term?

a)

100

b)

200

c)

50

d)

40

84.

If the b term is 18x, what is the new c term?

a)

9

b)

36

c)

225

d)

81

85.

Which is NOT a requirement for a trinomial to be a perfect square trinomial?

a)

the A and C terms must be perfect squares

b)

when factored the perfect square trinomial can be written as $\left(\ \ \ +\ \ \ \right)\left(\ \ \ -\ \ \ \right)$ or $\left(\ \ \ -\ \ \ \right)\left(\ \ \ +\ \ \ \right)$

c)

the square root of the A and C terms when multiplied together and doubled is the middle term

d)

the perfect square trinomial must have a positive C term

e)

when factored, the perfect square trinomial can be written as $\left(\ \ \ -\ \ \ \right)^2$ or $\left(\ \ \ +\ \ \ \right)^2$

86.

Split the following up and solve: $x=3\pm4$

a)

$x=6$ and $x=2$

b)

$x=7$ and $x=-1$

c)

$x=-2$ and $x=-6$

d)

$x=-7$ and $x=1$

Lessons 4-5 and 4-6

Total questions: 86

Worksheet time: 4hrs 9mins

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