Free Printable Factoring Review (or RETAKE)

1.

Factor using GCF or monomial factoring:

2n²-8n³

a)

2n²(n-4n²)

b)

2n²(1-4n)

c)

2n³(10-8n²)

d)

3n(1-4n)

2.

The factored form of m²+ 6m + 5 is

(m+2)(m+ 3)

a)

true

b)

false

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.

A rectangle has an area of 4x²+19x + 12 and a length of (x + 4). What is the width?

a)

4x - 3

b)

4x + 3

c)

2x + 6

d)

2x + 3

5.

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)

6.

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)

7.

Factor Completely:
x² - 36

a)

(x + 9)(x - 4)

b)

(x - 6)(x - 6)

c)

(x - 9)(x + 4)

d)

(x + 6)(x - 6)

8.

What do you call a polynomial that cannot be factored?

a)

FOIL

b)

Simplified

c)

Prime

d)

Proper

9.

Factor:
x² - 49

a)

(x + 7)(x - 7)

b)

(x + 7)²

c)

(x - 7)²

d)

(x+7)(x-1)

10.

6m² + 16m

a)

2(3m² + 8m)

b)

2m(3m + 8)

c)

2m(3m - 8m)

d)

not factorable

11.

Factor the following
12x³y⁴z²+14x⁴yz-6x⁵y⁴z²

a)

2x³yz(6xy³z+7x-3x²y³z)

b)

6x³yz(2y³z+2x-1x²y³z)

c)

2x²y²z(6y³z+7x-3x²y³z)

d)

2xyz(6x²y³z+7xyz-3x²y³z)

12.

Factor:
p² - 14p

a)

p(1 - 14)

b)

2p(p - 7)

c)

p²(1-14)

d)

p(p - 14)

13.

Which of the following binomials is not a difference of squares?

a)

x² - 64

b)

x² - 16

c)

x²+ 400

d)

x² - 100

14.

Which of the following is a correct rewriting or form of the binomial, x² - 169 ?

a)

(x + 13) (x - 13)

b)

(x + 13)²

c)

(x - 14) (x - 13)

d)

All of the above

15.

Factor x³ - 4x.

a)

(x-4)(x²-4)

b)

x(x-2)(x+2)

c)

x(x-4)

d)

(x-2)(x+2)

16.

4x²- 64y²

a)

Prime

b)

( 2x - 32y) (2 x + 32y)

c)

( 2x - 8y) (2 x - 8y)

d)

( 2x - 8y) (2 x + 8y)

17.

$6m^2+16m$

a)

$2(3m^2+8m)$

b)

$2m(3m+8)$

c)

$2m(3m-8m)$

d)

$not\ factorable$

18.

$6m^2+16m$

a)

$2(3m^2+8m)$

b)

$2m(3m+8)$

c)

$2m(3m-8m)$

d)

$not\ factorable$

19.

$p^2-14p$

a)

$p(1-14)$

b)

$2p(p-7)$

c)

$p2(1-14)$

d)

$p(p-14)$

20.

$4x^2-6x$

a)

$4x(x-2)$

b)

$2x(x-3)$

c)

$x(4x-6)$

d)

$2x(2x-3)$

21.

$3x+12x^2$

a)

$3x(1+4x)$

b)

$x(3x+12)$

c)

$3(x+4x)$

d)

$3x(4x)$

22.

$18x^2-9x$

a)

$18x(x-2)$

b)

$9x(9x-1)$

c)

$9x(2x-1)$

d)

$3x(6x-3)$

23.

$x^2-4x$

a)

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

b)

$x^2(x-4)$

c)

$4x(x-1)$

d)

$x(x-4)$

24.

$36x-9$

a)

$9(4x)$

b)

$3(12x-3)$

c)

$(6x+3)(6x-3)$

d)

$9(4x-1)$

25.

$18x^2+12x$

a)

$2x(9x+6)$

b)

$6x(3x+2)$

c)

$18x(x-6)$

d)

$12x(6x+1)$

26.

$x^2\ +\ 5x\ -\ 7\ =\ 0\$
What are the values of a, b, and c?

a)

$a\ =\ 1,\ b\ =\ 5,\ c\ =\ 7\$

b)

$a\ =\ 1,\ b\ =\ 5,\ c\ =\ -7\$

c)

$a\ =\ 0,\ b\ =\ 5,\ c\ =\ -7\$

d)

$a\ =\ 1,\ b\ =\ -5,\ c\ =\ -7\$

27.

$3x^2\ +\ 5x\ -\ 7\ =\ 3$
What are the values of a, b, and c?

a)

$a\ =\ 3,\ b\ =\ 5,\ c\ =\ -7$

b)

$a\ =\ 3,\ b\ =\ 5,\ c\ =\ -4\$

c)

$a\ =\ 3,\ b\ =\ 5,\ c\ =\ -10$

d)

$a\ =\ 3,\ b\ =\ 5,\ c\ =\ 7\$

28.

$56x^3\ -\ 8x$

a)

$8x^2(56x^3-8x)$

b)

$8x\left(7x^2-1\right)$

c)

$8x(7x^3-x)$

d)

$8x^2(35x^3-x)$

29.

Factor: x² + 24x + 144

a)

(x + 12)²

b)

(x + 9)²

c)

(x + 15)²

d)

(x + 13)²

30.

Factor: x² - 4x + 4

a)

(x + 2)²

b)

(x - 2)²

c)

(x + 4)²

d)

(x - 4)²

31.

Factor: x² - 30x + 225

a)

(x + 15)²

b)

(x - 15)²

c)

(x + 25)²

d)

(x - 25)²

32.

Factor

x² + 18x + 81

a)

(x + 9)(x – 9)

b)

(x + 18)²

c)

(x + 9)²

d)

(x + 6)²

33.

Solve by factoring:

x² + 2x - 24 = 0

a)

x = -6, x = 4

b)

x = 6, x = -4

c)

x = 12, x = -2

d)

x = 8, x = -3

34.

Convert x²- 9x + 20 = 0 to factored form and solve.

a)

(x-10)(x+2)=0; x = -2, 10

b)

(x+4)(x+5)=0; x = -5, -4

c)

(x-4)(x-5)=0; x = 4, 5

d)

Not factorable

35.

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

36.

Factor: 49x² - 100

a)

(49x + 100)(x - 1)

b)

(7x - 10)(7x + 10)

c)

(49x - 10)(x + 10)

d)

(7x -10)(7x - 10)

37.

Solve 5x²= 13x+6

a)

x = -3, x = 2/5

b)

x = -2, x = 15

c)

x = 3, x = -2/5

d)

x = 2, x = -15

38.

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

39.

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

40.

x² + 15x + 44 = 0

a)

{-8, 2}

b)

{-7, 5}

c)

{-11, -4}

d)

{-11}

41.

Solve the quadratic equation $x^2+7x=0$

Hint: Factor a GCF!!

4 lines

42.

Solve the equation by factoring.

a)

$\left\{-3,\ -4\right\}$

b)

$\left\{-6,\ -1\right\}$

c)

$\left\{8,\ 1\right\}$

d)

$\left\{-1,\ -2\right\}$

43.

Solve the equation by factoring.

a)

$\left\{2,\ -1\right\}$

b)

$\left\{-5,\ 5\right\}$

c)

$\left\{-4,\ 1\right\}$

d)

$\left\{-8,\ 6\right\}$

44.

What is the first question you ask yourself when factoring a polynomial?

a)

How many terms does it have?

b)

Is there a GCF?

c)

What strategy should I use?

d)

Why do I have to learn this?!?!?!

45.

Solve by factoring. z² + 81 = 18z

a)

z = 9

b)

z = -9

c)

z = 9 or z = -9

46.

Solve:

k² - 2k = 24

a)

k = -4, 6

b)

k = -4, -6

c)

k = -6, 1

d)

k = 4, -6

47.

Solve by factoring.

$6x^2+17x=24+7x$

a)

$\left\{\frac{3}{4},\ 3\right\}$

b)

$\left\{-1.4\right\}$

c)

$\left\{-\frac{4}{3},\ 3\right\}$

d)

$\left\{\frac{4}{3},\ -3\right\}$

e)

$\left\{-\frac{4}{3},\ 4\right\}$

48.

Solve
x² + 2x - 24 = 0

a)

x = -6, x = 4

b)

x = 6, x = -4

c)

x = 12, x = -2

d)

x = 8, x = -3

49.

Solve by factoring.

x² - 6x - 27 = 0

a)

x = 3 or x = 9

b)

x = 3 or x = -9

c)

x = -3 or x = 9

d)

x = -3 or x = -9

50.

Solve
2x² - 3x - 2 = 0

a)

x = 1, x = -1

b)

x = -1/2, x = 2

c)

x = 1/2, x = 2

d)

x = 1/2, x = 1

51.

What is the next step in solving after getting the quadratic in factored form?

(x + 2)(x - 3) = 0

a)

Plug in zero for x

b)

Multiply the binomials

c)

FOIL

d)

Set each binomial factor equal to zero

52.

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

53.

Select the solution(s) for the quadratic: $x^2-11x+19=-5$

a)

3

b)

8

c)

-9

d)

-3

54.

Find the solutions to 3x² + 18x +10= -5

a)

x = -5 and -1

b)

x = 5 and 1

c)

x = 0 and 5

d)

x = -2 and 4

55.

Solve:

3x² + 18x +15 = 0

Hint: Factor GCF first.

a)

x = 3, 2

b)

x = 5, 1

c)

x = -5, -1

d)

x = -3, -2

56.

Factor by using the GCF:

x² - 14x

a)

x(x - 14x)

b)

2x(x - 7)

c)

x²(x - 14)

d)

x(x - 14)

57.

Factor by GCF:

6x² + 16x

a)

2(3x² + 8x)

b)

2x(3x + 8)

c)

2x(3x + 8x)

d)

not factorable

58.

Factor using the GCF : -21x+35

a)

-7(3x - 5)

b)

7(-21x²+ 35)

c)

28(-3x²+ 5x)

d)

7(3x - 5)

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.

Find the product:
(3x – 1)(x + 5)

a)

3x² + 4x + 5

b)

3x² + 4x - 5

c)

3x² + 14x + 5

d)

3x² + 14x - 5

61.

Simplify:
(x-7)²

a)

x²-49

b)

x²+49

c)

x²-14x+49

d)

x²-14x-49

62.

(x+2)(x−2)

a)

x²−4x−4

b)

x²+4

c)

x²−4

d)

x²+4x−4

63.

Find the GCF: 6m² - 16m

a)

2

b)

2m

c)

2m²

d)

m

64.

Find the GCF: 8r³ + 16r²

a)

4r²

b)

8r²

c)

8

d)

4

65.

What is the GCF? 5x²+20x

a)

5

b)

x

c)

5x

d)

20x

66.

Factor:
56a³-8a

a)

8a²(56a³-8a)

b)

8a(7a²-1)

c)

8a(7a³-a)

d)

8a²(35a²-a)

67.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

68.

Factor
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

69.

What is the GCF? 5x²+20x

a)

5

b)

x

c)

5x

d)

20x

70.

Factor:
x² + 2x - 24

a)

(x - 6)(x + 4)

b)

(x + 6)(x + 4)

c)

(x - 6)(x - 4)

d)

(x + 6)(x - 4)

71.

Factor:
x² + 25x + 24

a)

(x + 5)(x + 5)

b)

(x + 24)(x + 1)

c)

(x + 12)(x + 2)

d)

(x + 8)(x + 3)

72.

What is the GCF? -5x-25

a)

x

b)

25

c)

-5

d)

-x

73.

What is the GCF? 12x+8

a)

12

b)

8

c)

4

d)

x

74.

x²+ 81

a)

Prime

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

( x - 9 ) ( x - 9 )

75.

Factor:
x² - 9

a)

(x + 3)(x - 3)

b)

(x + 3)²

c)

(x - 3)²

d)

(x+3)(x+3)

76.

Which is a common factor of 12x and 27?

a)

x

b)

12

c)

3

d)

9

77.

Factor using GCF or monomial factoring:

2n²-8n³

a)

2n²(n-4n²)

b)

2n²(1-4n)

c)

2n³(10-8n²)

d)

3n(1-4n)

78.

Factor out the GCF:
10x³ - 15x

a)

x(10x² - 15)

b)

5x(2x² - 3)

c)

5(2x³ - 3x)

d)

5x²(10x - 3)

79.

Factor using GCF or monomial factoring:

2x + 18

a)

2(x + 9)

b)

2(x + 8)

c)

2(2x + 9)

d)

cannot be factored

80.

Factor using GCF or monomial factoring:

x² - 5x

a)

1(x - 5)

b)

x(x - 5x)

c)

x(x - 5)

d)

x²(1 - 5)

81.

What is the GCF of the terms below?

24x³ + 36x²

a)

8x

b)

6x²

c)

12x²

d)

4x

e)

12x³

82.

Find the GCF of the terms of each polynomial.

72y⁵ + 18y²

a)

y²

b)

4y⁵

c)

18y

d)

18y²

83.

What is the greatest common factor of 20a²b² and 50b³?

a)

100a²b²

b)

10b³

c)

10ab²

d)

10b²

84.

Factor using GCF or monomial factoring:

w³ + 3w

a)

3w(1)

b)

w(w² + 3)

c)

w³(w + 3)

85.

Expand (x-2)(x-3)

a)

x² - 6x + 5

b)

x² - 6x - 5

c)

x² - 5x - 6

d)

x² - 5x + 6

86.

WHAT IS THE FACTOR OF 9X+45?

a)

9X

b)

9X(1+ 5)

c)

9(X+5)

d)

9(X+45)

87.

What is the factor of 6x²-24x?

a)

6x(x-4)

b)

6x(x-24x)

c)

6(x²-24x)

d)

6x²(1-24x)

88.

Which is a common factor of 12x and 27?

a)

x

b)

12

c)

3

d)

9

89.

Factor out the GCF:
10x³ - 15x

a)

x(10x² - 15)

b)

5x(2x² - 3)

c)

5(2x³ - 3x)

d)

5x²(10x - 3)

90.

Factor using GCF or monomial factoring:

2x + 18

a)

2(x + 9)

b)

2(x + 8)

c)

2(2x + 9)

d)

cannot be factored

91.

Factor using GCF or monomial factoring:

x² - 5x

a)

1(x - 5)

b)

x(x - 5x)

c)

x(x - 5)

d)

x²(1 - 5)

92.

GCF of 28 and 40

a)

2

b)

4

c)

7

d)

8

93.

Find the greatest common factor of 32 and 48

a)

2

b)

8

c)

16

d)

18

94.

It is a number, a variable or a combination of a number and a variable which can be found in each term of a given polynomial.

a)

Common Monomial Factor

b)

Difference of Two Squares

c)

Sum and Difference of Two Cubes

d)

Perfect Square Trinomials

95.

What is the common monomial factor of $6x^3+3x^2-12x$ ?

a)

$3$

b)

$2x$

c)

$3x$

d)

$3x^2$

96.

Factor
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

97.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

98.

Factor
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

99.

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)

100.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

101.

Factor
4n²-17n-15

a)

(n-10)(6n+1)

b)

(4n-5)(n-3)

c)

(n-5)(4n-3)

d)

(n-5)(4n+3)

102.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

103.

Factor
r² -16r + 60

a)

(r - 15)(r + 4)

b)

(r - 6)(r + 10)

c)

(r - 6)(r - 10)

d)

(r +30)(r - 2)

104.

Factor
x²-16x + 48

a)

(x - 12)(x - 4)

b)

(x + 6)(x - 8)

c)

(x + 12)(x - 4)

d)

(x -16)(x - 3)

105.

Factor:

2x² + 3x - 9

a)

2(x + 3)(x - 3)

b)

(2x - 3)²

c)

(x + 3)(2x - 3)

d)

(2x + 3)(x - 3)

106.

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)

107.

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)

108.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

109.

Factor
a² - a - 12

a)

(a - 4)(a + 3)

b)

(a + 6)(a - 4)

c)

(a - 6)(a + 4)

d)

(a + 4)(a - 3)

110.

Factor: m² - 81

a)

(m + 9)(m + 9)

b)

(m - 9)(m - 9)

c)

(m + 9)(m - 9)

d)

(m + 9)²

111.

Factor: a² - 50

a)

(a + 25)(a - 25)

b)

(a - 5)²

c)

(a - 25)²

d)

correct answer not given

112.

Factor:
n²+ 10n + 25

a)

(n + 5)(n - 5)

b)

(n + 25)(n + 1)

c)

(n - 5)²

d)

(n + 5)²

113.

Factor:
x² - 15x + 50

a)

(x - 10)(x - 15)

b)

(x - 10)(x - 5)

c)

(x - 25)²

d)

(x - 5)²

114.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

115.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

116.

Factor
a² - a - 12

a)

(a - 4)(a + 3)

b)

(a + 6)(a - 4)

c)

(a - 6)(a + 4)

d)

(a + 4)(a - 3)

117.

Factor
r² -16r + 60

a)

(r - 15)(r + 4)

b)

(r - 6)(r + 10)

c)

(r - 6)(r - 10)

d)

(r +30)(r - 2)

118.

Factor
x² - 5x - 36

a)

(x - 4)(x + 9)

b)

(x - 6)(x + 6)

c)

(x + 4)(x - 9)

d)

(x -12)(x + 3)

119.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

120.

x² - 9

a)

(x + 3)²

b)

(x + 3) (x - 3)

c)

(x - 3)²

d)

x + 3(x - 3)

121.

4x² - 25

a)

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

b)

(2x - 5)²

c)

(2x + 5)²

d)

2x + 5(2x - 5)

122.

Factor completely.

x² - 144

a)

( x - 12 ) ²

b)

( x - 12 ) ( x - 12 )

c)

( x + 12 ) ( x + 12 )

d)

( x + 12 ) ( x - 12 )

123.

Factor: x² + 24x + 144

a)

(x + 12)²

b)

(x + 9)²

c)

(x + 15)²

d)

(x + 13)²

124.

Factor: x² - 4x + 4

a)

(x + 2)²

b)

(x - 2)²

c)

(x + 4)²

d)

(x - 4)²

125.

Factor

x² + 18x + 81

a)

(x + 9)(x – 9)

b)

(x + 18)²

c)

(x + 9)²

d)

(x + 6)²

126.

Factor
n² + 5n - 6

a)

(n - 2)(n - 3)

b)

(n - 1)(n + 6)

c)

(n + 1)(n - 6)

d)

(n + 2)(n - 3)

127.

What is a method of checking your work when factoring?

a)

FOIL

b)

asking the teacher every time

c)

assume you're correct

d)

division

Factoring Review (or RETAKE)

Total questions: 127

Worksheet time: 8hrs 38mins

Similar Resources on Wayground