Free Printable Quadratics Part 2 Review

1.

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

a)

x-4

b)

x+4

c)

x+6

d)

x-2

2.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

3.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

4.

Factor
a² - a - 12

a)

(a - 4)(a + 3)

b)

(a + 6)(a - 4)

c)

(a - 6)(a + 4)

d)

(a + 4)(a - 3)

5.

Which of the following is a factor of
r² -16r + 60 ?

a)

r + 6

b)

r + 10

c)

r - 6

d)

r -30

6.

Factor
x²-16x + 48

a)

(x - 12)(x - 4)

b)

(x + 6)(x - 8)

c)

(x + 12)(x - 4)

d)

(x -16)(x - 3)

7.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

8.

Factor
9x²-6x-8

a)

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

b)

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

c)

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

d)

(x-1)(9x+8)

9.

Factor
4x²-25x+25

a)

4(x-5)(x+5)

b)

(x+5)(4x+5)

c)

(x-5)(4x-5)

d)

(x+2)(9x+1)

10.

Which of the following is a factor of
4n²-17n-15?

a)

n+5

b)

4n-5

c)

4n-3

d)

4n+3

11.

Factor:
2x² - 3x - 2

a)

(2x - 2)(x + 1)

b)

(2x + 1)(x - 2)

c)

(2x - 1)(x - 2)

d)

(2x - 1) (x - 1)

12.

Factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

13.

Factor
v² - 6v + 9

a)

(v-3)²

b)

(v-6)²

c)

(v-9)(v+6)

d)

not factorable

14.

Factor
x² + 4x + 3

a)

(x - 1)(x - 3)

b)

(x + 1)(x + 3)

c)

(x - 1)(x + 3)

d)

(x + 1)(x - 3)

15.

Which of the following is a factor of
x² - 9x + 20?

a)

x - 10

b)

x - 20

c)

x + 4

d)

x - 5

16.

Factor
x² + 11x + 24

a)

(x + 6)(x + 4)

b)

(x + 10)(x + 2)

c)

(x + 8)(x + 3)

d)

(x + 2)(x + 12)

17.

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)

18.

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)

19.

Factor:
x² - 9

a)

(x + 3)(x - 3)

b)

(x + 3)²

c)

(x - 3)²

d)

(x+3)(x+3)

20.

Which of the following is a factor of 3x² - 7x + 2?

a)

x - 1

b)

x - 2

c)

3x - 2

d)

3x + 1

21.

What is the Greatest Common Factor of 18 and 54?

a)

9

b)

6

c)

54

d)

18

e)

3

22.

15w - 3v

a)

5(3w - 3v)

b)

3w(5 - 3v)

c)

3(5w - v)

d)

3v(5w)

23.

7u²t² + 21ut² - ut

a)

7(u²t² + 3ut² - ut)

b)

ut(7ut + 21t - 1)

c)

u(7ut² + 21t² - t)

d)

t(7u²t + 21ut - u)

24.

Factor: 3x² + 4x

a)

x(3x + 4)

b)

3x(x + 4x)

c)

3(x² +4x)

d)

x²(3+4)

25.

Can this binomial be factored?

4x² + 7

a)

Yes

b)

No

26.

Can this binomial be factored?

5x - 4

a)

Yes

b)

No

27.

Can this binomial be factored?

x²+ 3x

a)

Yes

b)

No

28.

rn + 5n - r - 5

a)

(r - 1)(5 + n)

b)

(r + 5)(n - 1)

c)

r(n + 5n - 6)

d)

5r(n - 1)

29.

3np + 15p - 4n - 20

a)

(3p + 5)(n - 4)

b)

3p - 4(n + 5)

c)

(3p - 4)(n + 5)

d)

3p - 4 + n + 5

30.

Which of these is an example of additive inverse?

a)

-6a + 6ab

b)

12xy - 6xy

c)

20x - 15x - 5x

d)

-6x + 2x - 4x

31.

c - 2cd + 8d - 4

a)

c - 4(1 - 2d)

b)

(c - 1)(2d - 4)

c)

(c + 4) - (2d - 1)

d)

(c - 4)(1 - 2d)

32.

Solve by factoring:

x² = -10x

(a)

33.

Which of these is a solution to the graph?

a)

0

b)

1

c)

-1

d)

2

e)

-2

34.

Which of these is NOT another term for "solution" when we're talking about quadratics?

a)

y-intercept

b)

zero

c)

root

d)

x-intercept

35.

Solve using the quadratic formula :

x² - 7x + 12 = 0

a)

x = 3, -4

b)

x = -3, 4

c)

x = 3, 4

d)

x = -3, -4

36.

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

37.

Solve 8x² - 6x + 1 = 0

a)

No Solution

b)

0 or 1

c)

-0.5 or -0.25

d)

0.25 or 0.5

38.

The quadratic equation can be used to solve quadratic equations that cannot be factored.

a)

True

b)

False

39.

____________
For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

40.

What is the discriminant of -2x² − x − 1 = 0

a)

76

b)

-7

c)

9

d)

none of these

41.

20x³-25x²+4x-5

a)

(5x²-5)(4x+1)

b)

5(x²-1)(4x+5)

c)

(5x²+1)(4x-5)

d)

(5x²+1)(4x-1)

42.

30x³+15x²-18x-9

a)

(5x²-3)(6x+1)

b)

(5x²-3)(6x+3)

c)

3(5x²+3)(2x-1)

d)

3(5x²-3)(2x+1)

43.

Decide if (x-3) is a factor of 3x³+10x²-x-12

a)

Yes, it is a factor

b)

No, it is not a factor

44.

If 5 a factor of 27?

a)

yes

b)

no

45.

Is 5 a factor of 30?

a)

yes

b)

no

46.

Find all of the factor pairs of 24.

a)

1 x 24, 2 x 12

b)

1 x 24, 2 x 12, 3 x 8

c)

1 x 24, 4 x 6

d)

1 x 24, 2 x 12, 3 x 8, 4 x 6

47.

Select all the possible ways to make factor pairs of 54.

a)

1 x 57

b)

1 x 54

c)

2 x 27

d)

50 x 4

e)

3 x 18

48.

In the equation
y = x² +5x +7, match each leading coefficient with its correct letter

a)

a=0, b=5, c=7

b)

a=1, b=5, c=7

c)

a=7, b=5, c=1

49.

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.

50.

Solve Using the Quadratic Formula
2x² + 7x - 15 = 0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

51.

Identify the 'c' value: y = 16x² -8x -24

a)

16

b)

-8

c)

24

d)

-24

52.

Use the quadratic formula to find the solutions for
y = 3x³ + 8x - 1

a)

0.1167 and -2.7833

b)

.7 and -16.7

c)

.35 and -8.35

d)

0.2358 and -1.236

53.

Use the graph to determine the solutions.

a)

-1 and -3

b)

1 and -3

c)

1 and 3

d)

-1 and 3

54.

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

a)

True

b)

False

55.

Solve the quadratic equation.
3x²- 8x - 8 = 0

a)

A {0.38, -0.88}

b)

B {0.89, -8.9}

c)

C . {0.13, -0.63}

d)

D . {3.44, -0.77}

56.

Solve the quadratic equation.
3x²- 8x - 8 = 0

a)

A {0.38, -0.88}

b)

B {0.89, -8.9}

c)

C . {0.13, -0.63}

d)

D . {3.44, -0.77}

57.

Solve the quadratic equation.
2p² - 2p - 55 = 5

a)

A . {3.28, -2.28}

b)

B . {2.5, -1.78}

c)

C . {6, -5}

d)

D . {-1, 4}

58.

Solve for x. Round to the nearest hundredth if necessary.
3x² = 16x + 12

a)

x = -.67, 6

b)

x = -6, .67

c)

x = 3.33, 18

d)

x = -3.33, 18

59.

Identify the 'a' value: y = 16x² -8x -24

a)

16

b)

8

c)

-8

d)

-24

60.

Solve 2r² - 3r -5 = 0 using the quadratic formula

a)

x = 1/2, -2

b)

x = 5/2, -1

c)

x = 2, -1/2

d)

x = 1, -5/2

e)

No Solution

61.

Solve using the quadratic formula.
2x² - 9x - 35 = 0

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

62.

What is this formula?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

63.

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

64.

Which is the standard form for a quadratic equation?

a)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

b)

$ax^2+bx+c=0$

c)

$y=a\left(x-h\right)^2+k$

d)

$a^2+b^2=c^2$

65.

$2x^2=8x+3$

2x^2-8x-3=0

x=\frac{8\pm\sqrt{64-4\left(2\right)\left(-3\right)}}{4}

x=\frac{8\pm\sqrt{40}}{4}

x=\frac{8\pm2\sqrt{10}}{4}

x=\frac{4\pm\sqrt{10}}{2}

Suzanne solved the equation using this process.

Did she make a mistake?

If yes, at which line did she make her first mistake?

(There are 5 steps in her process)

a)

Suzanne made no errors.

b)

Step 2

c)

Step 3

d)

Step 4

e)

Step 5

66.

When using factoring to solve a quadratic equation, what must be true?

a)

The equation must be set equal to 1.

b)

The equation must be set equal to 10.

c)

The equation must be set equal to 0.

d)

It is not necessary to set the equation equal to anything.

67.

Solve using the quadratic formula :

x² - 7x + 12 = 0

a)

x = 3, -4

b)

x = -3, 4

c)

x = 3, 4

d)

x = -3, -4

68.

Solve using the Quadratic Formula 2x² + 7x - 15 = 0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

69.

Write in the standard form 7 + 2x = 5x²

a)

5x² + 2x + 7 = 0

b)

-5x² +2x + 7 = 0

c)

-5x² + 7 + 2x = 0

d)

2x + 7 + -5x² = 0

70.

If the discriminant is positive, then the solution will be

a)

one real solution

b)

two real solutions

c)

two non-real solutions

d)

all real numbers

71.

If the discriminant is negative, then the solution will be

a)

one real solution

b)

two real solutions

c)

two non-real solutions

d)

all real numbers

72.

Determine the value of the discriminant

x² + 7x + 13=0

a)

101

b)

3

c)

-101

d)

-3

73.

Describe the number and type solutions for the following:

x² + 7x + 13

a)

2 real solutions

b)

2 non-real solutions

c)

1 real solution

d)

1 non-real solution

74.

For the function below, what is the discriminant?

___________

x² + 8x + 16 = 0

a)

4

b)

-4

c)

0

d)

2

75.

For the function below, how many solutions are there?

___________

x² + 8x + 16 = 0

a)

2 real solutions

b)

2 non-real solutions

c)

1 real solution

d)

No solutions

76.

What is the discriminant of 6x² − 2x − 3 = 0

a)

76

b)

29

c)

-68

d)

none of these

77.

How many solutions?

6x² − 2x − 3 = 0

a)

2 real

b)

2 non-real

c)

1 real

d)

1 non-real

78.

x² - 9

a)

(x + 3) (x - 3)

b)

(x - 3) (x - 3)

c)

(x + 3) (x - 6)

d)

Can't factor using Diff. of Squares

79.

4a² - 25

a)

(2a + 5) (2a - 5)

b)

(2a - 5) (2a - 5)

c)

(x + 5) (x - 5)

d)

Can't factor using Diff. of Squares

80.

4m² + 49

a)

(2m + 7) (2m - 7)

b)

(2m - 7) (2m - 7)

c)

(m + 7) (m - 7)

d)

Can't factor using Diff. of Squares

81.

q² - 121

a)

(q + 11) (q - 11)

b)

(q - 11) (q - 11)

c)

(q + 11) (q + 11)

d)

Can't factor using Diff. of Squares

82.

r⁴ - q⁴

a)

(r² + q²) (r² - q²)

b)

(r² - q²) (r² - q²)

c)

(r + q) (r - q)

d)

Can't factor using Diff. of Squares

83.

r² - 9t²

a)

(r + 3t) (r - 3t)

b)

(r - 3t) (r - 3t)

c)

(3r + t) (3r - t)

d)

Can't factor using Diff. of Squares

84.

Which of these (more than one) are types of factorisation?

a)

Common Factor

b)

Quadratic

c)

Using Brackets

d)

Difference of Squares

e)

Expansion

85.

When factorising a trinomial that looks like this:

x^2-ax+b

The signs in the brackets should both be (a) .

86.

Factorise:

x^2+3x-130

a)

$\left(x+18\right)\left(x-15\right)$

b)

$\left(x-18\right)\left(x+15\right)$

c)

$\left(x-13\right)\left(x+10\right)$

d)

$\left(x+13\right)\left(x-10\right)$

87.

9x²- 49y⁶

a)

( 3x + 7y³) (3x + 7y³)

b)

( 3x - 7y³) (3x + 7y³)

c)

( 3x - 7y³) (3x - 7y³)

d)

Unfactorable

88.

x²+ 81

a)

Prime

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

( x - 9 ) ( x - 9 )

89.

32n² - 50
(Check for a GCF)

a)

(16n - 25)(16n + 25)

b)

2(8n - 25)(8n + 25)

c)

2(4n + 5)(4n - 5)

d)

Not Factorable

Quadratics Part 2 Review

Total questions: 89

Worksheet time: 5hrs 54mins

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