Free Printable Factorising Grade 10

1.

6m² + 16m

a)

2(3m² + 8m)

b)

2m(3m + 8)

c)

2m(3m - 8m)

d)

not factorable

2.

Factorise 4x + 14

a)

2(2x+7)

b)

4(x+10)

c)

4(x+3)

d)

2(x+12)

3.

Factorise 8x + 12

a)

4(x+2)

b)

8(x+4)

c)

4(x+3)

d)

4(2x+3)

4.

Factorise fully: 6x + 18

a)

3(2x + 6)

b)

6(x+3)

c)

2(3x+9)

d)

6(x+12)

5.

Factorsie fully: 20x + 30

a)

10(2x+3)

b)

10(x+3)

c)

5(4x+6)

d)

2(10x+15)

6.

Factorise fully 10x + 15

a)

5(x+3)

b)

2(5x+7)

c)

10(x+5)

d)

5(2x+3)

7.

Factorise fully 8x+32

a)

8(x+4)

b)

4(2x+16)

c)

2(4x+16)

d)

4(2x+8)

8.

Factorise fully: 27x + 45

a)

27(x+18)

b)

3(9x+15)

c)

9(3x+5)

d)

9(3x+36)

9.

Factorise fully: ab + 4b

a)

a(b+4)

b)

b(a+4)

c)

ab(1+4)

d)

b(a+4b)

10.

Factorise 6b + 8

a)

4(2b+2)

b)

2(3b+4)

c)

2(b+4)

d)

4(3b+2)

11.

Factorise fully: 18x + 24

a)

6(2x+4)

b)

2(9x+12)

c)

3(6x+8)

d)

6(3x+4)

12.

Factorise: 3x + 12

a)

3(x+4)

b)

3(x+5)

c)

3(3x + 9)

d)

3(x+9)

13.

Factorise: 4x² + 8x

a)

4x(x+2)

b)

4(x²+2x)

c)

2x(2x+4)

d)

2(2x²+4)

14.

Factorise: 12x² + 15x

a)

6x(2x+3)

b)

3(x²+5x)

c)

4x(3x+5)

d)

3x(4x+5)

15.

Factorise: 5x-10

a)

5(x-2)

b)

5(x+2)

c)

5(x-5)

d)

5(x+5)

16.

Factorise: 15y - 5

a)

5(3y+1)

b)

15(y-10)

c)

5(3y-1)

d)

5(y-3)

17.

Factorise fully: 6x² - 3x

a)

3x(2-x)

b)

3(2x²-x)

c)

3x(2x-1)

d)

6x(x-3)

18.

Factorise: 9x - 12

a)

4(3x - 3)

b)

3(3x - 4)

c)

3x(x - 4)

d)

9(x-3)

19.

Factorise fully: 18 - 6x

a)

3(2x - 3)

b)

3(6 - 2x)

c)

6(3 - x)

d)

6(x - 3)

20.

12x + 9

a)

3(4x + 3)

b)

x(12+9)

c)

3(4x - 3)

d)

not factorable

21.

Factorise
x² + 8x + 12

a)

(x + 3)(x + 4)

b)

(x + 6)(x + 2)

c)

(x + 4)(x + 4)

d)

(x + 1)(x + 12)

22.

Factorise
x² + 15x + 36

a)

(x + 6)(x + 6)

b)

(x + 9)(x +4)

c)

(x + 4)(x + 9)

d)

(x + 12)(x + 3)

23.

Factorise
x² + 8x

a)

(x + 2)(x + 4)

b)

(x + 8)(x + 1)

c)

x(x + 8)

d)

2x(x + 4)

24.

Factorise
x² + 4x - 12

a)

(x + 6)(x - 2)

b)

(x - 4)(x + 2)

c)

(x - 6)(x + 2)

d)

(x - 6)(x - 2)

25.

Factorise
x² - 6x - 16

a)

x(x - 6)

b)

(x - 8)(x - 2)

c)

(x + 2)(x - 8)

d)

(x - 4)(x - 4)

26.

Factorise
x² - 8x + 12

a)

(x - 12)(x + 4)

b)

(x + 6)(x - 2)

c)

(x + 6)(x + 2)

d)

(x - 2)(x - 6)

27.

Factorise
x² - 7x + 6

a)

(x - 6)(x - 1)

b)

(x + 4)(x + 2)

c)

(x + 1)(x + 6)

d)

(x - 10)(x + 3)

28.

Factorise
2x² + 9x + 10

a)

(x + 10)(2x + 1)

b)

(2x +10)(x - 1)

c)

(2x + 5)(x + 2)

d)

(x + 1)(x + 10)

29.

Factorise
3x² + 7x - 20

a)

(3x + 2)( x -10)

b)

(3x - 5)(x + 4)

c)

(x + 20)(3x - 1)

d)

(3x - 5)(x - 4)

30.

Factorise
6x² - 19x + 20

a)

(3x - 4)(2x - 5)

b)

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

c)

(3x + 2)(2x - 10)

d)

(3x + 2)(2x + 10)

31.

Factorise the expression:

x² + x - 6

a)

(x + 3)(x - 2)

b)

(x + 2)(x - 3)

c)

(x + 6)(x - 1)

d)

(x + 1)(x - 6)

32.

Factorise the expression:

x² + 5x + 6

a)

(x + 3)(x + 2)

b)

(x + 2)(x - 3)

c)

(x + 5)(x + 1)

d)

(x - 2)(x - 3)

33.

Factorise the expression:

x² + 9x + 20

a)

(x + 4)(x + 5)

b)

(x - 4)(x - 5)

c)

(x + 3)(x + 6)

d)

(x - 3)(x - 6)

34.

Factorise the expression:

x² + 10x + 9

a)

(x + 4)(x + 5)

b)

(x + 1)(x + 9)

c)

(x - 1)(x + 10)

d)

(x + 3)(x + 6)

35.

Factorise the expression:

x² - 7x + 12

a)

(x + 3)(x + 4)

b)

(x - 3)(x - 4)

c)

(x - 3)(x + 4)

d)

(x + 3)(x - 4)

36.

Factorise the expression:

x² - 2x - 24

a)

(x + 6)(x - 4)

b)

(x - 6)(x + 4)

c)

(x - 12)(x + 2)

d)

(x - 6)(x - 4)

37.

Factorise the expression:

x² - 6x - 27

a)

(x - 9)(x - 3)

b)

(x - 9)(x + 3)

c)

(x - 3)(x + 9)

d)

(x + 3)(x + 9)

38.

Factorise the expression:

x² + 5x - 24

a)

(x + 8)(x - 3)

b)

(x + 3)(x - 8)

c)

(x + 6)(x - 4)

d)

(x + 4)(x - 6)

39.

Factorise the expression:

x² + 8x + 16

a)

(x + 4)²

b)

(x + 3)(x + 5)

c)

(x - 4)²

d)

(x + 8)(x + 2)

40.

Factorise the expression:

x² + 7x - 78

a)

(x + 13)(x - 6)

b)

(x + 26)(x - 3)

c)

(x - 13)(x + 6)

d)

(x + 3)(x - 26)

41.

Expand and simplify the following quadratic expression...

(x + 4)(x + 6)

a)

x² + 10x + 24

b)

x² + 10x + 10

c)

x² + 24x + 10

d)

x² + 24x + 24

42.

Expand and simplify the following quadratic expression...

(x + 3)(x + 2)

a)

x² + 5x + 6

b)

x² + 5x + 5

c)

x² + 6x + 6

d)

x² + 6x + 5

43.

Expand and simplify the following quadratic expression...

(x + 3)(x + 8)

a)

x² + 11x + 24

b)

x² + 11x + 11

c)

x² + 24x + 11

d)

x² + 24x + 24

44.

Expand and simplify the following quadratic expression...

(x - 8)(x + 8)

a)

x² + 16x - 64

b)

x² + 16x + 64

c)

x² - 16x + 64

d)

x² - 64

45.

Expand and simplify the following quadratic expression...

(x - 6)(x + 5)

a)

x² + x - 30

b)

x² - x - 30

c)

x² + x + 30

d)

x² - x + 30

46.

Expand and simplify the following quadratic expression...

(x - 6)(x - 4)

a)

x² - 10x + 24

b)

x² - 10x - 24

c)

x² + 10x - 24

d)

x² + 10x + 24

47.

Factorise the following quadratic expression...

x² + 14x + 24

a)

(x + 12)(x + 2)

b)

(x + 8)(x + 3)

c)

(x + 4)(x + 6)

d)

(x + 24)(x + 1)

48.

Factorise the following quadratic expression...

x² + 12x + 32

a)

(x + 16)(x + 2)

b)

(x + 8)(x + 4)

c)

(x + 6)(x + 6)

d)

(x + 32)(x + 1)

49.

x² - 9

a)

(x + 3)²

b)

(x + 3) (x - 3)

c)

(x - 3)²

d)

x + 3(x - 3)

50.

x² - 16

a)

(x + 4) (x - 4)

b)

(x + 8) (x - 2)

c)

(x + 4)²

d)

x + 4(x - 4)

51.

4x² - 25

a)

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

b)

(2x - 5)²

c)

(2x + 5)²

d)

2x + 5(2x - 5)

52.

25x² - 36y²

a)

5x + 6y(5x - 6y)

b)

(5x + 6y) (5x - 6y)

c)

(5x + 6y)²

d)

(5x - 6y)²

53.

4x²y² - 1

a)

(2 + xy) (2 - xy)

b)

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

c)

(2xy + 1) (2xy - 1)

d)

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

54.

64x² - 81y²

a)

(8x + 7y) (8x - 7y)

b)

(8x + 9y) (8x - 9y)

c)

(6x + 7y) (6x - 7y)

d)

(6x + 9y) (6x - 9y)

55.

4x² - 16

a)

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

b)

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

c)

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

d)

4(x + 2) (x - 2)

56.

49x² - 144y²

a)

(7x + 16y) (7x - 16y)

b)

(7x + 12y)²

c)

(12x + 7y) (12x - 7y)

d)

(7x + 12y) (7x - 12y)

57.

x⁴ - 100y²

a)

(x² + 10y) (x² - 10y)

b)

(x + 10y) (x - 10y)

c)

(x + 10y) (x³ - 10y)

d)

(x³ + 10y) (x - 10y)

58.

121x²y⁶z⁸ - 225w⁴

a)

(11xy⁴z⁴ + 15w) (11xy²z⁴ - 15w)

b)

(11x²y³z⁴ + 15w) (11x²y³z⁴ - 15w)

c)

(11xy³z⁴ + 15w²) (11xy³z⁴ - 15w²)

d)

(11xy³z + 15w²) (11xy³z³ - 15w²)

59.

We can't factor using difference of two square this

49x² + 4y². Why?

a)

Because 4 is not a perfect cubed number.

b)

Because 4 is not a perfect squared number.

c)

Because 49 is not a perfect squared number.

d)

Because we can't factor using difference of two squares if it is addition sign.

60.

We can't factor using difference of two square this

25x² - 51y². Why?

a)

Because 51 is not a perfect cubed number.

b)

Because 51 is not a perfect squared number.

c)

Because 25 is not a perfect squared number.

d)

Because we can't factor using difference of two squares if it is addition sign.

61.

Which one is false about the difference of two squares?

a)

We can factor that it is addition sign.

b)

We can factor that it is a perfect squared number (Example: x², 25, 49)

c)

Formula: a² - b² = (a + b) (a - b)

d)

We can factor that it is minus sign.

62.

Which of these can factor using difference of two squares?

a)

144x² - 49y²

b)

x² + 4x - 12

c)

100x² + 20x + 1

d)

14x - 16

63.

x² − 7x − 18

a)

(x − 9)(x + 2)

b)

(x + 9)(x + 2)

c)

(x − 9)(x - 2)

d)

(x − 9)(x - 2)

64.

p² − 5p − 14

a)

( p + 2)( p + 7)

b)

( p + 2)( p − 7)

c)

( p - 2)( p − 7)

d)

( p - 2)( p + 7)

65.

m² − 9m + 8

a)

(m + 1)(m − 8)

b)

(m − 1)(m + 8)

c)

(m − 1)(m − 8)

d)

(m + 1)(m + 8)

66.

x² − 16x + 63

a)

(x + 9)(x + 7)

b)

(x − 9)(x + 7)

c)

(x + 9)(x − 7)

d)

(x − 9)(x − 7)

67.

7k² + 9k

a)

k(7k - 9)

b)

k(7k + 9)

c)

7k(k + 9)

d)

(k+3)(7k + 3)

68.

7x² − 45x − 28

a)

7(x + 4)(x − 7)

b)

(x + 4)(7x - 7)

c)

(7x + 4)(x − 7)

d)

(7x - 4)(x + 7)

69.

2b² + 17b + 21

a)

(2b + 7)(b + 3)

b)

(2b + 3)(b - 7)

c)

2(b + 3)(b + 7)

d)

(2b + 3)(b + 7)

70.

5p² − p − 18

a)

5(p + 9)( p − 2)

b)

(p + 9)( 5p − 2)

c)

(5p - 9)( p + 2)

d)

(5p + 9)( p − 2)

71.

7x² − 32x − 60

a)

(7x + 10)(x − 6)

b)

7(x + 10)(x − 6)

c)

(7x - 10)(x − 6)

d)

(7x - 10)(x + 6)

72.

9r² − 5r − 10

a)

(9r + 2)(r - 5)

b)

(3r + 2)(3r - 5)

c)

9(r + 2)(r - 5)

d)

not factorable

73.

9x² + 7x − 56

a)

(3x + 7)(3x - 8)

b)

9(x + 7)(x - 8)

c)

(3x - 7)(3x - 8)

d)

not factorable

74.

Factor completely: 3x²-36x+96

a)

(x-4)(x-8)

b)

3(x-4)(x-8)

c)

3(x+1)(x+32)

d)

3(x-2)(x+16)

75.

Factor completely: 2x²+22x+60

a)

(2x+10)(x+6)

b)

(x+5)(x+6)

c)

2(x+1)(x+30)

d)

2(x+5)(x+6)

76.

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)

77.

Which of the following is a difference of squares?

a)

x² - 18

b)

4x² + 36

c)

9x² - 100

d)

x² + 4

78.

What are the factors of
25x² - 81?

a)

(5x - 9)(5x + 9)

b)

(5x - 9)(5x - 9)

c)

(5x + 9)(5x + 9)

d)

Cannot be factored

79.

Factor 4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

80.

Solve

h² + 7h + 10 = 0

a)

A. h= -5 or h= -2

b)

B. h= 5 or h= 2

c)

C. h = -1 or h= ^-10/₆

d)

D. h = ^-2/₅, or h= -10

81.

Factor the following expression

10x³ - 15x

a)

x(10x² - 15)

b)

5x(2x² - 3)

c)

5(2x³ - 3x)

d)

5x²(10x - 3)

82.

Factor:
x² - 9

a)

(x + 3)(x - 3)

b)

(x + 3)²

c)

(x - 3)²

d)

(x+3)(x+3)

83.

Factor Completely.
8x³ - 18x

a)

2x(4x²-9)

b)

(4x²+3)(2x-3)

c)

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

d)

PRIME

84.

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)

85.

Factor by grouping:
x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

86.

3b(9b-27)=0

a)

{-3,3}

b)

{0,3}

c)

{-3,9}

d)

{3,3}

87.

12x + 9

a)

3(4x + 3)

b)

x(12+9)

c)

3(4x - 3)

d)

not factorable

88.

Find the factors of 5x²+20x+20

a)

5(x+2)(x+2)

b)

5(x-2)(x-2)

c)

5(x+2)(x-2)

d)

(5x+2)(x+2)

89.

Factor Completely: x⁴-9x²

a)

x²(x+3)(x-3)

b)

(x²+3x)(x²-3x)

c)

(x²+9)(x-3)(x+3)

d)

x²(x²-9)

90.

What is the factored form of 5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

91.

Factor p³- 3p² - 16p + 48

a)

p² ( p - 3) (p - 3)

b)

(p² - 16) (p - 3)

c)

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

92.

x³-5x²+5x-25

a)

(x²-5)(x-5)

b)

(x²+5)(x-5)

c)

(x²+5)(x+5)

d)

(x²-1)(x-25)

93.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

94.

6m² + 16m

a)

2(3m² + 8m)

b)

2m(3m + 8)

c)

2m(3m - 8m)

d)

not factorable

95.

Factorise 4x + 14

a)

2(2x+7)

b)

4(x+10)

c)

4(x+3)

d)

2(x+12)

96.

Factorise 8x + 12

a)

4(x+2)

b)

8(x+4)

c)

4(x+3)

d)

4(2x+3)

97.

Factorise fully: 6x + 18

a)

3(2x + 6)

b)

6(x+3)

c)

2(3x+9)

d)

6(x+12)

98.

Factorsie fully: 20x + 30

a)

10(2x+3)

b)

10(x+3)

c)

5(4x+6)

d)

2(10x+15)

99.

Factorise fully 10x + 15

a)

5(x+3)

b)

2(5x+7)

c)

10(x+5)

d)

5(2x+3)

100.

Factorise fully 8x+32

a)

8(x+4)

b)

4(2x+16)

c)

2(4x+16)

d)

4(2x+8)

101.

Factorise fully: 27x² + 45x³

a)

27(x+18)

b)

3x²(9+15x)

c)

9x²(3 + 5x)

d)

9(3x+5)

102.

Factorise fully: ab + 4b²

a)

a(b+4)

b)

b²(a+ 4)

c)

ab(1+ 4)

d)

b(a+4b)

103.

Factorise -6b - 8

a)

4(2b+2)

b)

-2(3b + 4)

c)

2(b+4)

d)

2(3b - 4)

104.

Factorise fully: 18x + 24

a)

6(2x+4)

b)

2(9x+12)

c)

3(6x+8)

d)

6(3x+4)

105.

Factorise: 3x + 12x³- 6x²

a)

3(x+ 4x²- 2)

b)

3(x+ 5 - 6x²)

c)

3x(1 + 4x² - 2x)

d)

3x(x+ 4x² -2x)

106.

Factorise: 4x² + 8x

a)

4x(x+2)

b)

4(x²+2x)

c)

2x(2x+4)

d)

2(2x²+4)

107.

Factorise: 12x² + 15x

a)

6x(2x+3)

b)

3(x²+5x)

c)

4x(3x+5)

d)

3x(4x+5)

108.

Factorise: -5x +10

a)

-5(x - 2)

b)

5(x+2)

c)

5(x - 5)

d)

5(x + 5)

109.

Factorise: 15y - 5

a)

5(3y+1)

b)

15(y-10)

c)

5(3y-1)

d)

5(y-3)

110.

Factorise fully: 6x² - 3x

a)

3x(2-x)

b)

3(2x²-x)

c)

3x(2x-1)

d)

6x(x-3)

111.

Factorise: 9x - 12

a)

4(3x - 3)

b)

3(3x - 4)

c)

3x(x - 4)

d)

9(x-3)

112.

Factorise fully: 18 - 6x

a)

3(2x - 3)

b)

3(6 - 2x)

c)

6(3 - x)

d)

6(x - 3)

113.

12x + 9

a)

3(4x + 3)

b)

x(12+9)

c)

3(4x - 3)

d)

not factorable

114.

-4u(2b - 4u)

a)

-8ub + 16 u²

b)

-8ub + 16u

c)

ub + 16u²

d)

8ub + 16u²

115.

Which of the following is the correct expansion of:
3p(4p - 7q)?

a)

7p - 10pq

b)

12pq - 21q²

c)

9q

d)

12p² - 21pq

116.

Which of the following is equivalent to 5x + 23

a)

5(x + 5) - 2

b)

5(x + 23)

c)

5(x + 15) + 3

d)

5(x + 4) + 6

117.

Expand 3(4d - 3)

a)

12d - 9

b)

7d - 6

c)

34d - 33

d)

12d² - 9

118.

Expand 3z(4z + 6)

a)

12z² + 18z

b)

34z² + 18

c)

12z² + 18

d)

12z² - 18z

119.

Factorise
x² + 8x + 12

a)

(x + 3)(x + 4)

b)

(x + 6)(x + 2)

c)

(x + 4)(x + 4)

d)

(x + 1)(x + 12)

120.

Factorise
x² + 15x + 36

a)

(x + 6)(x + 6)

b)

(x + 9)(x +4)

c)

(x + 4)(x + 9)

d)

(x + 12)(x + 3)

121.

Factorise
x² + 4x - 12

a)

(x + 6)(x - 2)

b)

(x - 4)(x + 2)

c)

(x - 6)(x + 2)

d)

(x - 6)(x - 2)

122.

Factorise
x² - 6x - 16

a)

x(x - 6)

b)

(x - 8)(x - 2)

c)

(x + 2)(x - 8)

d)

(x - 4)(x - 4)

123.

Factorise
x² - 8x + 12

a)

(x - 12)(x + 4)

b)

(x + 6)(x - 2)

c)

(x + 6)(x + 2)

d)

(x - 2)(x - 6)

124.

Factorise
x² - 7x + 6

a)

(x - 6)(x - 1)

b)

(x + 4)(x + 2)

c)

(x + 1)(x + 6)

d)

(x - 10)(x + 3)

125.

Factorise the expression:

x² + x - 6

a)

(x + 3)(x - 2)

b)

(x + 2)(x - 3)

c)

(x + 6)(x - 1)

d)

(x + 1)(x - 6)

126.

Factorise the expression:

x² + 5x + 6

a)

(x + 3)(x + 2)

b)

(x + 2)(x - 3)

c)

(x + 5)(x + 1)

d)

(x - 2)(x - 3)

127.

Factorise the expression:

x² + 9x + 20

a)

(x + 4)(x + 5)

b)

(x - 4)(x - 5)

c)

(x + 3)(x + 6)

d)

(x - 3)(x - 6)

128.

Factorise the expression:

x² + 10x + 9

a)

(x + 4)(x + 5)

b)

(x + 1)(x + 9)

c)

(x - 1)(x + 10)

d)

(x + 3)(x + 6)

129.

Factorise the expression:

x² - 7x + 12

a)

(x + 3)(x + 4)

b)

(x - 3)(x - 4)

c)

(x - 3)(x + 4)

d)

(x + 3)(x - 4)

130.

Factorise the expression:

x² - 2x - 24

a)

(x + 6)(x - 4)

b)

(x - 6)(x + 4)

c)

(x - 12)(x + 2)

d)

(x - 6)(x - 4)

131.

Factorise the expression:

x² - 6x - 27

a)

(x - 9)(x - 3)

b)

(x - 9)(x + 3)

c)

(x - 3)(x + 9)

d)

(x + 3)(x + 9)

132.

Factorise the expression:

x² + 5x - 24

a)

(x + 8)(x - 3)

b)

(x + 3)(x - 8)

c)

(x + 6)(x - 4)

d)

(x + 4)(x - 6)

133.

Factorise the expression:

x² + 8x + 16

a)

(x + 4)²

b)

(x + 3)(x + 5)

c)

(x - 4)²

d)

(x + 8)(x + 2)

134.

Fully factorise $x^2-121$

(a)

135.

Fully factorise $x^2-4$

(a)

136.

Fully factorise $5x^2+13x+6$

(a)

137.

Fully factorise $2x^2+20x+42$

(a)

138.

Fully factorise $9x^2+22x+8$

(a)

139.

Fully factorise $16x^2-25$

(a)

140.

Fully factorise the following $x^3+16x^2+63x$

(a)

141.

Fully factorise $8x^2+14x+5$

(a)

142.

Fully factorise $5x^2-30x+40$

(a)

143.

$49x^2-1$

(a)

144.

Fully factorise $5x^2+13x-6$

(a)

145.

Fully factorise $x^3-7x^2-18x$

(a)

146.

Fully factorise $81x^2-4$

(a)

147.

Fully factorise $7x^2-19x-6$

(a)

148.

Fully factorise $12x^2-2x-4$

(a)

149.

Fully factorise $25x^3-x$

(a)

150.

Fully factorise $10x^2-11x-6$

(a)

151.

Fully factorise $10x^2-11x-6$

(a)

152.

Fully factorise $100x^3-36x$

(a)

153.

Fully factorise $100x^3-210x^2-100x$

(a)

154.

$5n³-10n²+3n-6$

a)

$(5n²+3)(n-2)$

b)

$(5n²-3)(n-2)$

c)

$(5n³+3)(n-2)$

d)

$10n(n²-6)$

155.

$4p^3+8p^2+3p+6$

a)

$(2p^2+3)(p+2)$

b)

$(2p^2+6)(p+4)$

c)

$(4p^2+3)(p+2)$

d)

$(4p^2+8p)(3p+6)$

156.

a)

A

b)

B

c)

C

d)

D

157.

a)

A

b)

B

c)

C

d)

D

158.

a)

A

b)

B

c)

C

d)

D

159.

Factorise : x²- 9

a)

(x-3)(x-3)

b)

(x-3)(x+3)

c)

(x-3)(3-x)

d)

(x-3)²

160.

x²+ 2x +1

a)

(x+1)²

b)

(x-1)²

c)

(x+1)(x-1)

d)

none of these

161.

(x²- 8x +16)

a)

(x+4)²

b)

(x-4)²

c)

(x+4)(x-4)

d)

can not be factorised.

162.

x²+ 15x + 50

a)

(x+3)(x+5)

b)

(x+30)(x+20)

c)

(x+30)(x-20)

d)

(x+5)(x+10)

163.

x²y²- 25

a)

(xy + 5) ²

b)

(xy + 5)(xy - 5)

c)

(xy -5)(xy - 5)

d)

can not be factorised

164.

m² + 9x + 14

a)

(m+3)²

b)

(m-3)²

c)

(m+2)(m+7)

d)

(m+4)(m+10)

165.

(m^.m - 4m - 77)

a)

(m+4)(m+7)

b)

(m-11)(m+7)

c)

(m+11)(m-7)

d)

(m+11)(m+7)

166.

Factorise $-2x^2+10x+28$

Do not use any spaces!

(a)

167.

Factorise $121-16y^2$

Do not use any spaces!

(a)

168.

Factorise
x² + 15x + 36

a)

(x + 6)(x + 6)

b)

(x + 9)(x +4)

c)

(x + 4)(x + 9)

d)

(x + 12)(x + 3)

169.

Factorise
x² + 8x + 12

a)

(x + 3)(x + 4)

b)

(x + 6)(x + 2)

c)

(x + 4)(x + 4)

d)

(x + 1)(x + 12)

170.

Factorise
x² + 15x + 36

a)

(x + 6)(x + 6)

b)

(x + 9)(x +4)

c)

(x + 4)(x + 9)

d)

(x + 12)(x + 3)

171.

Factorise
x² + 4x - 12

a)

(x + 6)(x - 2)

b)

(x - 4)(x + 2)

c)

(x - 6)(x + 2)

d)

(x - 6)(x - 2)

172.

Factorise
x² - 6x - 16

a)

x(x - 6)

b)

(x - 8)(x - 2)

c)

(x + 2)(x - 8)

d)

(x - 4)(x - 4)

173.

Factorise
x² - 8x + 12

a)

(x - 12)(x + 4)

b)

(x + 6)(x - 2)

c)

(x + 6)(x + 2)

d)

(x - 2)(x - 6)

174.

Factorise
x² - 7x + 6

a)

(x - 6)(x - 1)

b)

(x + 4)(x + 2)

c)

(x + 1)(x + 6)

d)

(x - 10)(x + 3)

175.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

176.

Factor
n² + 5n - 6

a)

(n - 2)(n - 3)

b)

(n - 1)(n + 6)

c)

(n + 1)(n - 6)

d)

(n + 2)(n - 3)

177.

Factor
a² - a - 12

a)

(a - 4)(a + 3)

b)

(a + 6)(a - 4)

c)

(a - 6)(a + 4)

d)

(a + 4)(a - 3)

178.

Factor
r² -16r + 60

a)

(r - 15)(r + 4)

b)

(r - 6)(r + 10)

c)

(r - 6)(r - 10)

d)

(r +30)(r - 2)

179.

Factor
x²-16x + 48

a)

(x - 12)(x - 4)

b)

(x + 6)(x - 8)

c)

(x + 12)(x - 4)

d)

(x -16)(x - 3)

180.

Factor:
v² + 3v - 88

a)

(v + 11)(v - 8)

b)

(v + 22)(v - 4)

c)

(v + 8)(v - 11)

d)

(v - 22)(v + 4)

181.

Factor:
x²-15x + 36

a)

(x - 18)(x + 2)

b)

(x - 12)(x - 3)

c)

(x - 12)(x + 3)

d)

(x + 18)(x - 2)

182.

Factor
x² +17x - 60

a)

(x - 20)(x + 3)

b)

(x + 12)(x - 5)

c)

(x - 12)(x + 5)

d)

(x + 20)(x - 3)

183.

Factorise
2x² + 9x + 10

a)

(x + 10)(2x + 1)

b)

(2x +10)(x - 1)

c)

(2x + 5)(x + 2)

d)

(x + 1)(x + 10)

184.

Factorise
3x² + 7x - 20

a)

(3x + 2)( x -10)

b)

(3x - 5)(x + 4)

c)

(x + 20)(3x - 1)

d)

(3x - 5)(x - 4)

185.

Factorise
6x² - 19x + 20

a)

(3x - 4)(2x - 5)

b)

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

c)

(3x + 2)(2x - 10)

d)

(3x + 2)(2x + 10)

186.

Factor completely,

6x^2-18x-60

4 lines

187.

Expand,

\left(2x-1\right)\left(x-3\right)

4 lines

188.

Factor,

x^2-64

4 lines

189.

Expand,

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

4 lines

190.

Factor,

2x^2+3x-20

4 lines

191.

Factor

32-18y^2

4 lines

192.

What

\frac{x^2-5x+6}{x-3}

be equal to?

4 lines

193.

$x\left(y+4\right)-2\left(y+4\right)$

a)

$\left(y+4\right)\left(x-2\right)$

b)

$\left(xy+4\right)\left(2y-8\right)$

c)

$\left(y-4x\right)\left(2+x\right)$

d)

$\left(x+4\right)\left(y-2\right)$

194.

$a^2b^2-400$

a)

$\left(ab-20\right)^2$

b)

$\left(ab-100\right)\left(ab+100\right)$

c)

$ab\left(ab-400\right)$

d)

$\left(ab+20\right)\left(ab-20\right)$

195.

$10p^2+30+p^3+3p$

a)

$10\left(p^2+3\right)+p\left(p^2+3\right)$

b)

$p\left(10p+30+p^2+3\right)$

c)

$\left(p+10\right)\left(p+3\right)$

d)

$\left(p^2+3\right)\left(10+p\right)$

196.

$w^2-10w+25$

a)

$\left(w-5\right)^2$

b)

$\left(w-5\right)\left(w+5\right)$

c)

$\left(w+5\right)^2$

d)

$\left(w-12\right)\left(w+2\right)$

197.

$3b^2+21b-90$

a)

$3\left(b^2+7b-30\right)$

b)

$3\left(b+10\right)\left(b-3\right)$

c)

$3b\left(b+7\right)-90$

d)

$3\left(b+15\right)\left(b-2\right)$

198.

$5x^2+7x+2$

a)

$\left(5x+5\right)\left(5x+2\right)$

b)

$\left(x+2\right)\left(x+5\right)$

c)

$\left(5x+2\right)\left(x+1\right)$

d)

$\left(x+7\right)\left(x+2\right)$

199.

$4d+12-de-3e$

a)

$4\left(d-3\right)-e\left(d-3\right)$

b)

$\left(d-3\right)\left(4-e\right)$

c)

$4\left(d+3\right)-e\left(d+3\right)$

d)

$\left(d+3\right)\left(4-e\right)$

200.

$4n^2+12n+8$

a)

$4\left(n+1\right)\left(n+2\right)$

b)

$\left(4n+4\right)\left(4n+2\right)$

c)

$4\left(n+1\right)\left(4n+3\right)$

d)

$\left(2n+4\right)\left(2n+2\right)$

201.

$y^4-1$

a)

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

b)

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

c)

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

d)

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

202.

Simplify:

$\frac{4}{d^2-2}\div\frac{8}{d+2}$

a)

$\frac{1}{2\left(d-2\right)}$

b)

$\frac{1}{2\left(d+2\right)}$

c)

$\frac{2}{d-2}$

d)

$\frac{2}{d+2}$

203.

Simplify:

$\frac{x^2-5x+6}{x^3-4x}\times\frac{2x^2-8\ }{y^2+y}$

a)

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

b)

$\frac{2\left(y-6\right)}{y^2}$

c)

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

d)

$\frac{y-6}{2y^2}$

204.

Simplify:

$\frac{y-4}{y^2-8y+16}$

a)

$y+4$

b)

$\frac{1}{y+4}$

c)

$y-4$

d)

$\frac{1}{y-4\ }$

205.

$2x^2-11x-6$

a)

$\left(2y-1\right)\left(y+6\right)$

b)

$\left(2y+1\right)\left(y-6\right)$

c)

$\left(2y-12\right)\left(2y+1\right)$

d)

$\left(2y-1\right)\left(2y+12\right)$

206.

a)

4a/2

b)

2a

c)

3a/2

d)

4a/4

207.

a)

10a/10b

b)

10a/5b

c)

2a/b

d)

a/b

208.

a)

a/2

b)

3a/6

c)

8a/6

d)

7a/6

209.

a)

(2k-6l )/12

b)

(4k-12l )/24

c)

(k-3l)/6

d)

(3d-2l)/24

210.

a)

8m²/8n²

b)

13m/4n

c)

13m²/4n²

d)

8m/8n

211.

a)

4/p

b)

5/p

c)

14/p²

d)

4/p²

212.

a)

a²/6

b)

2a/3a

c)

3a/2a

d)

3/2

213.

Fully Factorise

5x²+20x+20

a)

5(x+2)(x+2)

b)

5(x-2)(x-2)

c)

5(x+2)(x-2)

d)

(5x+2)(x+2)

214.

Fully Factorise

2c² + 2c - 84

a)

(c-6)(2c+14)

b)

(c+7)(2c-12)

c)

(c-4)(2c+21)

d)

2(c+7)(c-6)

215.

Fully Factorise

4x² - 20x + 25

a)

(4x - 25) (x -1)

b)

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

c)

(2x - 5)²

d)

(4x - 5) (x - 5)

216.

Fully Factorise

3x²- 75

a)

3( x + 5 ) ( x - 5 )

b)

Prime

c)

( x + 5 ) ( x - 5 )

d)

3( x - 5 ) ( x - 5 )

217.

Fully Factorise

16x² + 18x + 12

a)

4(4x² + 6x + 3)

b)

2(8x² + 9x + 6)

c)

2x(8x + 9 + 3)

d)

x(16x + 18 + 12)

218.

Fully Factorise

21z² - 70z + 49

a)

7(3z - 7)(z - 1)

b)

7(3z + 7)(z + 1)

c)

7(3z - 7)(z + 1)

d)

7(3z + 7)(z - 1)

219.

Fully Factorise

-2h² + 4h + 70

a)

-2(h + 7)(h + 5)

b)

-2(h - 7)(h - 5)

c)

-2(h + 7)(h - 5)

d)

-2(h - 7)(h + 5)

220.

Fully Factorise

5g² + 15g + 10

a)

5(g + 2)(g + 1)

b)

(5g + 10)(5g + 5)

c)

5(g + 5)(g + 2)

d)

5(g - 1)(g - 2)

221.

Fully Factorise

3x^2+9x-30

a)

$\left(3x+5\right)\left(x-4\right)$

b)

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

c)

$3\left(x-2\right)\left(x+5\right)$

d)

$3\left(x^2+3x-10\right)$

222.

Fully Factorise

2x^2-10x+12

a)

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

b)

$2\left(x-5\right)\left(x+1\right)$

c)

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

d)

$2\left(x-6\right)\left(x+5\right)$

223.

Complete the formula
a³-b³=

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

224.

Complete the formula

a³+b³=

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

225.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

226.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

227.

Factor
27x³-64

a)

(3x-4)(9x²+12x+16)

b)

(3x-4)(9x²-12x+16)

c)

(3x+4)(9x²-12x+16)

d)

(3x+4)(9x²+12x+16)

228.

Fully Factor the Following
8x³-27

a)

(2x+3)(4x²-6x+9)

b)

(2x-3)(4x²+6x+9)

c)

(2x-3)(4x²+6x-9)

d)

(2x-3)(2x²+6x+9)

229.

Factor using differencesum/ of cubes. (use your notes!)
a³ + b³

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

230.

Which number is both a perfect square and a perfect cube?

a)

64

b)

27

c)

81

d)

16

231.

Identify if the expression can be factored as sum or difference of cubes:

3x³ + 24

a)

No

b)

Yes

c)

Yes, getting GCF first

d)

It is a sum of squares

232.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

233.

Factor: 27x³ + 8

a)

(3x + 2)(9x² - 6x + 4)

b)

(9x + 2)(3x² + 18x + 4)

c)

(3x²+4)(9x + 2)

d)

(27x + 8)(x² - 216x + 64)

234.

Fully Factor the Following
216x³+125

a)

6(x+5)³

b)

(6x+5)³

c)

(6x+5)(6x²-30x+25)

d)

(6x+5)(36x²-30x+25)

235.

Factor this sum of cubes:
2x³ + 128

a)

2(x³ + 64)

b)

(x + 4)(x² - 4x + 16)

c)

2(x - 4)(x² + 4x + 16)

d)

2(x + 4)(x² - 4x + 16)

236.

Factor this sum of cubes:
216x³ + 125

a)

6(x + 5)³

b)

(6x - 5)(36x² + 30x + 25)

c)

(6x + 5)(6x² - 30x + 25)

d)

(6x + 5)(36x²- 30x + 25)

237.

x³ + 27

a)

(x + 3)(x² - 3x + 9)

b)

(x + 2)(x² - 2x + 4)

c)

(x + 4)(x² - 4x + 16)

d)

(x - 3)(x² + 3x + 9)

238.

x³ - 27

a)

(x - 4)(x² + 4x + 16)

b)

(x + 3)(x² - 4x + 16)

c)

(x - 1)(x² + 1x + 1)

d)

(x - 3)(x² + 3x + 9)

239.

8x³ + 27

a)

(3x - 2)(9x² + 6x + 4)

b)

(3x - 1)(9x² + 3x + 1)

c)

(2x + 3)(4x² - 6x + 9)

d)

(2x - 1)(4x² + 2x + 1)

240.

125x³ - 64

a)

(5x - 4)(25x² + 20x + 16)

b)

(5x + 2)(25x² - 10x + 4)

c)

(3x - 1)(9x² + 3x + 1)

d)

(4x - 3)(16x² + 12x + 9)

241.

x³ + 64

a)

(x + 3)(x² - 3x + 9)

b)

(x + 5)(x² - 5x + 25)

c)

(x + 4)(x² - 4x + 16)

d)

(x - 4)(x² + 4x + 16)

242.

x³ - 64

a)

(x - 4)(x² + 4x + 16)

b)

(x - 3)(x² + 3x + 9)

c)

(x - 5)(x² + 5x + 25)

d)

(x + 4)(x² - 4x + 16)

243.

125x³ + 8

a)

(5x - 4)(25x² + 20x + 16)

b)

(5x + 2)(25x² - 10x + 4)

c)

(4x + 1)(16x² + 4x + 1)

d)

(4x - 3)(16x² + 12x + 9)

244.

27x³ - 1

a)

(3x - 1)(9x² + 3x + 1)

b)

(2x - 1)(4x² + 2x + 1)

c)

(3x - 2)(9x² + 6x + 4)

d)

(4x + 1)(16x² + 4x + 1)

245.

x³ + 27

a)

(x + 3)(x² - 3x + 9)

b)

(x + 2)(x² - 2x + 4)

c)

(x + 4)(x² - 4x + 16)

d)

(x - 3)(x² + 3x + 9)

246.

8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(3x - 1)(9x² + 3x + 1)

c)

(3x - 2)(9x² + 6x + 4)

d)

(x - 3)(4x² - 6x + 9)

247.

64x³ + 1

a)

(4x - 3)(16x² + 12x + 9)

b)

(3x - 1)(9x² + 3x + 1)

c)

(2x - 1)(4x² + 2x + 1)

d)

(4x + 1)(16x² - 4x + 1)

248.

What is ALWAYS the first step when factoring?

a)

Look for the HCF

b)

Write a, b, and c

c)

Difference of squares

d)

Use FOIL

249.

We can't factor using difference of two square this

49x² + 4y². Why?

a)

Because 4 is not a perfect cubed number.

b)

Because 4 is not a perfect squared number.

c)

Because 49 is not a perfect squared number.

d)

Because we can't factor using difference of two squares if it is addition sign.

250.

Factor completely.

49x² + 16

a)

( 7x + 4 ) ( 7x - 4 )

b)

( 7x + 4 ) ( 7x + 4 )

c)

( 7x - 4 ) ²

d)

cannot be factored (SUM of squares)

251.

Which of these can be factored using difference of two squares?

a)

144x² - 49y²

b)

x² + 4x - 12

c)

100x² + 20x + 1

d)

14x - 16

Factorising Grade 10

Total questions: 251

Worksheet time: 7hrs 39mins

Similar Resources on Wayground