Free Printable Factorization Including Quadratic Expressions

1.

Factorise $4uv-3v$

a)

$v\left(4u-3\right)$

b)

$4v\left(u-3\right)$

c)

$u\left(4v-3v\right)$

d)

$4uv\left(3v\right)$

2.

Factorise $6x^2+12x$

a)

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

b)

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

c)

$6x\left(x+2\right)$

d)

$x\left(6x+12\right)$

3.

Factorise $4xy-6xz$

a)

$x\left(4y-6z\right)$

b)

$2x\left(2y-3z\right)$

c)

$2\left(2xy-3xz\right)$

d)

$4x\left(y-6z\right)$

4.

Factorise $2x^2-6xy$

a)

$2x\left(x-3y\right)$

b)

$2x\left(x-6y\right)$

c)

$2x^2\left(1-6y\right)$

d)

$2x^2\left(6y\right)$

5.

Factorise $5x^2-7x$

a)

$5x-7$

b)

$5x\left(x-7\right)$

c)

$5\left(x^2-7x\right)$

d)

$x\left(5x-7\right)$

6.

Factorise $3y^2-7xy$

a)

$3\left(y^2-7xy\right)$

b)

$3y\left(y-7x\right)$

c)

$y\left(3y-7x\right)$

d)

$y^2\left(3\right)-y\left(7x\right)$

7.

Factorise $6g^2-3g^3$

a)

$3\left(2g^2-g^3\right)$

b)

$3g\left(2g-g^2\right)$

c)

$3g^2\left(2-g\right)$

d)

$g^2\left(6-3g\right)$

8.

Factorise $xy^2-x^2y$

a)

$x\left(y^2-xy\right)$

b)

$y\left(xy-x^2\right)$

c)

$xy\left(y-x\right)$

d)

$xy^2\left(1-x\right)$

9.

$\ factorize.\ -3x^2\ -9x$

a)

$-3x\left(x+3\right)$

b)

$3x\left(x+3\right)$

c)

$3x\left(-x-3\right)$

d)

$-3\left(x^2\ +3x\right)$

10.

$factorize.\ 2\pi r^2+2\pi rh$

a)

$2\pi r^2\left(1+h\right)$

b)

$\ 2\left(\pi r^2+\pi rh\right)$

c)

$2r\left(\pi r+\pi h\right)$

d)

$2\pi r\left(r+h\right)$

11.

$FACTORIZE\ \ \ a^2b^3-a^5b^2+2a^4b^6$

a)

$a^2b^2\left(1-b^3+2a^2b^4\right)$

b)

$a^2b^2\left(b-a^3+2a^2b^4\right)$

c)

$a^2b^2\left(b+a^3-2a^2b^4\right)$

d)

$a^2b^2\left(1+b^3-2a^2b^4\right)$

12.

$FACTORIZE\ \ \ \ a\left(3x+2\right)+2\left(3x+2\right)$

a)

$\left(3x+2\right)\left(a+1\right)$

b)

$\left(3x+2\right)\left(a\right)$

c)

$\left(3x+2\right)\left(a-2\right)$

d)

$\left(3x+2\right)\left(a+2\right)$

13.

$FACTORIZE\ \ \ \ 2h\left(5a+2\right)-\left(5a+2\right)$

a)

$\left(5a+2\right)\left(2h\right)$

b)

$\left(5a+2\right)\left(2h+1\right)$

c)

$\left(5a+2\right)\left(2h-1\right)$

d)

$\left(5a-2\right)\left(2h-1\right)$

14.

$factorize\ \ \ 3a\left(x-3\right)-6k\left(x-3\right)$

a)

$3ax-9a-6kx+18k$

b)

$\left(3a-6k\right)1$

c)

$\left(x-3\right)\left(3a-6k\right)$

d)

$3\left(x-3\right)\left(a-2k\right)$

15.

$\ FACTORIZE\ \ \ \ ax-5a+4x-20$

a)

$\left(x+5\right)\left(a-4\right)$

b)

$\left(x-5\right)\left(a+4\right)$

c)

$5x-25a$

d)

$6a-20ax$

16.

$FACTORIZE\ \ \ \ \ x^3-x^2-1+x$

a)

$\left(x-1\right)\left(x^2+1\right)$

b)

$\left(x^3-1\right)\left(-x^2+x\right)$

c)

$\left(x^2+1\right)\left(1-x\right)$

d)

$\left(x^2-1\right)\left(x+1\right)$

17.

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

a)

$\left(a+2b\right)\left(9b+2a\right)$

b)

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

c)

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

d)

$\left(a+2b\right)\left(9b-2a\right)$

18.

$FACTORIZE\ \ \ \ 3bc-bd-2ad+6ac$

a)

$\left(d-3c\right)\left(b+2a\right)$

b)

$\left(3c+d\right)\left(b-2a\right)$

c)

$\left(3c-d\right)\left(b+2a\right)$

d)

$\left(d-3c\right)\left(b-2a\right)$

19.

$FACTORIZE\ \ 5x^2+5xy-15x-15y$

a)

$\left(5x-15\right)\left(x+y\right)$

b)

$\left(5x+15\right)\left(x_{\ }-y\right)$

c)

$5\left(x+3\right)\left(x-y\right)$

d)

$5\left(x-3\right)\left(x+y\right)$

20.

$FACTORIZE\ \ \ \ m^3+m^2\left(2m-1\right)$

a)

$m^2\left(3m-1\right)$

b)

$m^2\left(m+1\right)$

c)

$m^2\left(m^2+2m-1\right)$

d)

$m^3\left(2m-1\right)$

21.

The factorisation of 12a²b+15ab² gives:

a)

3ab(4ab+5)

b)

3ab(4a+5b)

c)

3a(4a+5b)

d)

3b(4a + 5b)

22.

The factorisation of 12x+36 is

a)

12(x+3)

b)

12(3x)

c)

12(3x+1)

d)

x(12+36x)

23.

On factorising 14pq + 35pqr, we get:

a)

pq(14+35r)

b)

p(14q+35qr)

c)

q(14p+35pr)

d)

7pq(2+5r)

24.

The factors of 6xy – 4y + 6 – 9x are:

a)

(3x + 2) (2y + 3)

b)

(3x – 2) (2y – 3)

c)

(3x – 2) (2y + 3)

d)

(3x –+2) (2y – 3)

25.

The factors of x²+xy+8x+8y are:

a)

(x+y) (x+8)

b)

(2x+y) (x+8)

c)

(x+2y) (x+8)

d)

(x+y) (2x+8)

26.

The factors of 4y² – 12y + 9 is

a)

(2y+3)²

b)

(2y-3)²

c)

(2y-3)(2y+3)

d)

None of the above

27.

The factors of 49p² – 36 are:

a)

(7p+6)²

b)

(7p-6)²

c)

(7p – 6 ) ( 7p + 6)

d)

None of the above

28.

The factors of m² – 256 are:

a)

(m + 4)²

b)

(m – 4)²

c)

(m – 4) (m+4)

d)

None of the above

29.

The factors of m² – 256 are:

a)

(m + 4)²

b)

(m – 4)²

c)

(m – 4) (m+4)

d)

None of the above

30.

When we factorise x²+5x+6, then we get:

a)

(x +2) (x + 3)

b)

(x – 2) (x – 3)

c)

(x × 2) + (x × 3)

d)

(x × 2) – (x × 3)

31.

The factors of 3m² + 9m + 6 are:

a)

(m + 1) (m + 2)

b)

3(m + 1) (m + 2)

c)

6(m + 1) (m + 2)

d)

9(m + 1) (m + 2)

32.

Which of the following is equal to x³ – 225x

a)

x(1 – 15x) (1 + 15x)

b)

x(x – 15) (x + 15)

c)

x(1 – 15x) (1 – 15x)

d)

x(1 + 15x) (1 – 15x).

33.

Which of the following are the factors of a² + ab +bc + ca

a)

(b + c) (c + a)

b)

(a + b) (a + c)

c)

a(a + b + c)

d)

(a + b) (b + c).

34.

Which of the following is the common factor of: 5xy, 3pqr and 40 xyz?

a)

5

b)

0

c)

xy

d)

1

35.

Which are the factors in common of

20ab²-5ab-10a³b

a)

5ab

b)

5a³b²

c)

5a³b

d)

None of these

36.

Factorise

k²-2k+1

a)

(k⁴+2)²

b)

(k²+1)²

c)

(k-1)²

d)

None of these

37.

The factors of m² – 256 are:

a)

(m + 4)²

b)

(m – 4)²

c)

(m – 4) (m+4)

d)

(m – 16) (m + 16)

38.

Factor: x² + 2x – 3

a)

(x - 2)(x + 1)

b)

(x + 1)(x - 3)

c)

(x + 2)(x - 1)

d)

(x - 1)(x + 3)

39.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

40.

Factor
x² + x - 6

a)

(x + 2)(x + 3)

b)

(x + 6)(x -1)

c)

(x + 3)(x - 2)

d)

(x +1)(x - 6)

41.

Factor
a² - a - 12

a)

(a - 4)(a + 3)

b)

(a + 6)(a - 4)

c)

(a - 6)(a + 4)

d)

(a + 4)(a - 3)

42.

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)

43.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

44.

4x²- 64y²

a)

Prime

b)

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

c)

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

d)

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

45.

25x²y²- 100

a)

( 5xy - 10) (5xy + 10)

b)

( 5xy + 10) (5xy + 10)

c)

Prime

d)

( 5xy - 50) (5xy + 50)

46.

9x²- 49y⁶

a)

( 3x + 7y³) (3x + 7y³)

b)

( 3x - 7y³) (3x + 7y³)

c)

( 3x - 7y³) (3x - 7y³)

d)

Prime

47.

x²+ 81

a)

Prime

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

( x - 9 ) ( x - 9 )

48.

Factor p³- 3p² - 16p + 48

a)

p² ( p - 3) (p - 3)

b)

(p² - 16) (p - 3)

c)

(p + 4) (p - 4) (p - 3)

49.

What is the factored form of x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

50.

What are the solutions of the equation x²+8x+15=0? (Solve by factoring)

a)

-5,-3

b)

-3,5

c)

-5,3

d)

3,5

51.

What are the solutions to this equation?
(3x-2)(5x+1)=0

a)

x=5/2,-1/3

b)

x=1/5,-2/3

c)

x=1/3,-5/2

d)

x=2/3,-1/5

52.

Solve for x. Round to the nearest hundredth if necessary.
3x²= 27

a)

x = 9

b)

x = 3

c)

x = -3, 3

d)

x = x = -9, 9

53.

The solutions of the quadratic equation
x²+2x-15=0 are

a)

x = 3 or x = 5

b)

x = 5 or x = -3

c)

x = -5 or x = 3

d)

x = -3 or x = -5

54.

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

55.

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)

56.

x²- 400

a)

( x - 200) ( x + 200)

b)

( x + 20) ( x + 20)

c)

Prime

d)

( x - 20) ( x + 20)

57.

Simplify the product. Write the answer in standard form.
(x+2)(x-5)

a)

x²-3x-10

b)

2x²-3

c)

x²-10

d)

x²+2x-10

58.

Which are the factors in common of

20ab²-5ab-10a³b

a)

5ab

b)

5a³b²

c)

5a³b

59.

Are there any common factors? What are they?

4x²(2w-3)-5(2w-3)

a)

4x²

b)

2w

c)

(2w-3)

60.

Identify the common factors of

13m²y⁵-39my³-26y²

a)

13my²

b)

13y²

c)

13m²y⁵

61.

Factorise

(a+3)(a+1)-4(a+1)

a)

(a+1)(a+3-4)

b)

(a+1)(a-1)

c)

(a-1)(a-1)

62.

Factorise

k²-2k+1

a)

(k⁴+2)²

b)

(k²+1)²

c)

(k-1)²

63.

Factorise

4 - a²

a)

(a+2)(a-2)

b)

(2a+a)(2a-1)

c)

(2+a)(2-a)

d)

(a²+2)(a²+2)

64.

FACTORISE

m² + 3m + 2

a)

(m + 2)(m + 3)

b)

(m + 2)(m + 1)

c)

(m + 3)

d)

(m + 4)(m - 3)

65.

FACTORISE:

6x² + 13x + 6

a)

(6x + 6)(x + 1)

b)

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

c)

(x + 5)(4x + 4)

d)

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

66.

FACTORISE

4x²- 25

a)

(4x²-25)(4x²+25)

b)

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

c)

(2x+5)²

67.

FACTORISE

ax + bx + x

a)

x(a + b + 1)

b)

x(a + b)

c)

x(x + b + a)

d)

x(x + b + 1)

68.

FACTORISE

x²-11x+30

a)

(x-6)(x-5)

b)

(x-6)(x+5)

c)

(x-6)(x+5)

d)

IMPOSIBLE

69.

FactoriSE

3a²b + 3ab²

a)

3a(b + 2b)

b)

3(ab + ab²)

c)

3ab(a + b)

d)

3a²b(1 + b)

70.

All odd numbers are prime

a)

True

b)

False

71.

All even numbers are composite

a)

True

b)

False

72.

What is the greatest common factor of 36 and 54

a)

2

b)

6

c)

9

d)

18

73.

What is the greatest common factor of 60 and 75

a)

2

b)

5

c)

15

d)

25

74.

What is the greatest common factor of 36 and 40

a)

2

b)

9

c)

4

d)

8

75.

Stickers come in packs of 12. Notebooks come in packs of 10. What is the fewest number of packs of each item that Lindsay can buy in order to have the same number of each item.

a)

10 packs of stickers; 12 packs of notebooks

b)

5 packs of stickers; 6 packs of notebooks

c)

6 packs of stickers; 5 packs of notebooks

d)

60 packs of each

76.

What is the standard form of 2² x 3² x 5

a)

120

b)

180

c)

90

d)

140

77.

What is the Prime Factorization of 460?

a)

2² x 5 x 23

b)

2²x 5³

c)

2² x 3 x 5 x 23

d)

3²x 5 x 23

78.

Using a Factor Tree, find the prime factorization of 75.

a)

5² x 3

b)

5 x 5 x 3

c)

3² x 5

d)

15 x 5

79.

Write 36 as the product of it's prime factors...

a)

2 x 2 x 3 x 3

b)

2 x 2 x 2 x 3

c)

2² x 3²

d)

2² x 3

80.

Find the prime factorization for 80

a)

4²⋅ 5

b)

2⁴⋅ 5

c)

2 ⋅ 2 ⋅ 2

d)

8 ⋅ 5 ⋅ 2

81.

What is the prime factorization of 16 ?

a)

1 x 16

b)

2²x 4

c)

2⁴

d)

2² + 2²

82.

Which is the prime factorization of 12 ?

a)

2 x 6

b)

2 + 2 + 2 + 2 + 2 + 2

c)

2²x 3

d)

1 x 2²x 3

83.

One is...

a)

prime

b)

composite

c)

not prime or composite

d)

the loneliest number

84.

A composite number ...

a)

has more than 2 factors.

b)

has one factor.

c)

has at least 10 factors.

d)

is always a really big number.

85.

A prime number...

a)

has one factor.

b)

has more than 2 factors.

c)

has 100 factors.

d)

has exactly 2 factors: 1 and the itself.

Factorization Including Quadratic Expressions

Total questions: 85

Worksheet time: 5hrs 47mins

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