FACTORING BY GROUPING WORKSHEET

Fully factorise :

Problem 1 :

ab + ac – 2a

Solution

Problem 2 :

a2b2 – 2ab

Solution

Problem 3 :

18x – 2x3

Solution

Problem 4 :

x2 + 14x + 49

Solution

Problem 5 :

4a3 – 4ab2

Solution

Problem 6 :

x3y – 4xy

Solution

Problem 7 :

4x4 – 4x2

Solution

Problem 8 :

(x - 2)y – (x - 2)z

Solution

Problem 9 :

(x + 1)a + (x + 1)b

Solution

Problem 10 :

(x - y)a + (x - y)

Solution

Problem 11 :

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

Solution

Problem 12 :

x3 + x2 + x + 1

Solution

Factorise completely :

Problem 13 :

7x - 35y

Solution

Problem 14 :

2g2 - 8

Solution

Problem 15 :

-5x2 - 10x

Solution

Problem 16 :

m2 + 3mp

Solution

Problem 17 :

a2 + 8a + 15

Solution

Problem 18 :

m2 - 6m  + 9

Solution

Problem 19 :

5x2 + 5xy - 5x2y

Solution

Problem 20 :

xy + 2x + 2y + 4

Solution

Problem 21 :

y2 + 5y - 9y - 45

Solution

Problem 22 :

2x2 + 10x + x + 5

Solution

Problem 23 :

3y2 - 147

Solution

Problem 24 :

3p2 - 3q2

Solution

Problem 25 :

4c2 - 1

Solution

Problem 26 :

3x2 + 3x - 36

Solution

Problem 27 :

2bx - 6b + 10x - 30

Solution

Fully factorise :

Problem 28 :

12 - 11x - x2

Solution

Problem 29 :

-2x2 - 6 + 8x

Solution

Problem 30 :

14 - x2 - 5x

Solution

Problem 31 :

4x2 - 2x3 - 2x

Solution

Problem 32 :

(a + b)2 - 9

Solution

Problem 33 :

(x + 2)2 - 4

Solution

Answer Key

1)  a(b + c - 2)

2)  ab(ab - 2)

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

4)  (x + 7)2

5)  4a(a + b) (a - b)

6)  xy(x + 2) (x - 2)   

7)   4x(x + 1) (x - 1)

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

9) (x + 1)[a + b]

10)  (x - y)(a + 1)

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

12)  (x2 + 1) (x + 1)

13)  7(x - 5y)

14) 2(g2 - 4)

15)  -5x(x + 2)

16) m(m + 3p)

17)  (a + 3) (a + 5)

18) (m - 3)2

19) 5x(x + y - xy)

20) (x + 2) (y + 2)

21)  (y - 9) (y + 5)

22) (2x + 1) (x + 5)

23) 3(y + 7) (y - 7)

24) 3(p + q) (p - q)

25) (2c - 1) (2c + 1)

26) 3(x - 3) (x - 4)

27)  2(x - 3) (b + 5)

28) -(x + 12) (x - 1)

29)  -2(x - 1) (x - 3)

30)  -(x + 7) (x - 2)

31)  -2x(x - 1)2

32)  (a + b - 3) (a + b + 3)

33)  x (x + 4)

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