Preliminary Mathematics Worksheet
Factorising
NSW Syllabus Ref: 1.3

© Mathematics Plus, 2002

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Question 1

Factorise:

I

II

III

(a)

3x + 6

(a)

12x + 6

(a)

8 - 2x

(b)

x2 + x

(b)

2u3 - u

(b)

2x2 + 4x

(c)

4xy + 2x

(c)

8a - 12ab

(c)

12x2y - 30y

(d)

ab + ab2

(d)

2xy + 6xy2

(d)

4x2y + 10xy2

(e)

ax + a

(e)

a2x - a

(e)

ax - aby

(f)

4x + 2y + 6z

(f)

a2x + a2 + a

(f)

2x3 + 4x2 - 2x

Question 2

Factorise these expressions:

I

II

(a)

3(x + 5) + x(x + 5)

(a)

9a(a - 3) - 7a(a - 3)

(b)

x(a + b) + y(a + b)

(b)

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

(c)

3(a + b) + (a + b)2

(c)

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

Question 3

Factorise (grouping in pairs):

I

II

(a)

ax + bx + ay + by

(a)

ax + ay - cx - cy

(b)

ax + 3x - 3y - ay

(b)

8ax - 6x + 12ay - 9y

(c)

10ax + 5ay + 2bx + by

(c)

12ax - 8bx + 15ay - 10by

(d)

ay + 2a + 3y + 6

(d)

2xy + y - 2x - 1

(e)

y2 + 2y + ay + 2a

(e)

2x2 - 6x + ax - 3a

(f)

uv - 4u - 3v + 12

(f)

2ax - 6bx + 3ay - 9by

(g)

2x2 + yx - 2ax - ay

(g)

x3 - 2x2 + 3x - 6

(h)

mx - nx - my + ny

(h)

2ax2 - 2ay2 - bx2 + by2

(i)

2a3 + ba2 + 4ab + 2b2

(i)

5x3 - 2y2x - 5x2y + 2y3

(j)

x2y2 - axy + 2xy - 2a

(j)

a3b2 + a2bx - abx - x2

(k)

(a + b)2 + a + b

(k)

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

Question 4

Factorise (difference of squares):

I

II

III

(a)

x2 - 25

(a)

x2 - y2

(a)

x2 - 5

(b)

a2 - 36

(b)

(b)

1 - m2

(c)

4x2 - 49

(c)

4 - 9a2

(c)

2x2 - 1

(d)

25b2 - 4a2

(d)

9x2 - 4y2

(d)

(e)

(e)

(e)

x2y2 -a2

(f)

(x - 1)2 - 25

(f)

(p - q)2 - 1

(f)

4(a + 2)2 - 9

(g)

(3x + 1)2 - y2

(g)

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

(g)

4(x+1)2 - (y-3)2

(h)

a4 - 16

(h)

x4 - y4

(h)

16x4 - 81y4


Question 5

Factorise (Monic trinomials):

I

II

III

(a)

x2 + 3x + 2

(a)

a2 + 6a + 5

(a)

m2 + 8m + 12

(b)

x2 + 11x + 18

(b)

x2 + 14x + 45

(b)

6 + 5y + y2

(c)

a2 - 7a + 10

(c)

y2 - 7y + 12

(c)

x2 - 16x + 28

(d)

p2 - 7p + 12

(d)

x2 - 8x + 15

(d)

p2 - 2pq + q2

(e)

y2 - 10y  - 24

(e)

x2 - 8x - 20

(e)

u2 + 7u - 60

(f)

x2 + 2x + 1

(f)

t2 - 10t  + 25

(f)

16 - 8u + u2

(g)

y2 - 6y  + 9

(g)

m2 + 2mn +n2

(g)

x2 + 2ax + a2

(h)

u2 + 13u + 36

(h)

x2 - 2x - 15

(h)

x2 - 2xy - 15y2

(i)

q2 - 12q + 36

(i)

a2 + 3a - 18

(i)

a2 + 3ab - 18b2

(j)

a2 - a - 132

(j)

u2 - 14u - 120

(j)

x2 + (a+1)x + a

 

Question 6

Factorise (Non-monic trinomials):

I

II

III

(a)

2x2 + 3x + 1

(a)

2x2 - 3x + 1

(a)

2x2 + x - 1

(b)

2x2 + 5x + 2

(b)

2x2 - 5x + 2

(b)

3y2 + 8y + 5

(c)

4a2 - 7a + 3

(c)

6y2 + 19y +14

(c)

2x2 - 11x + 12

(d)

5p2 - 21p + 4

(d)

4u2 + 3u - 1

(d)

9p2 + 13p - 10

(e)

3y2 - 11y  + 6

(e)

3x2 - 17x + 20

(e)

2u2 - 29u + 60

(f)

5x2 - 17x - 12

(f)

9t2 - 12t + 4

(f)

7 - 4x - 3x2

(g)

3x2 + x - 4

(g)

12n2 + 29n - 8

(g)

12x2 + x - 6

(h)

9u2 - 12u + 4

(h)

10t2 - 29t +10

(h)

9 + 3u - 2u2

(i)

10a2 - 3a - 18

(i)

2 + 3q - 9q2

(i)

4x2 + 4xy + y2

(j)

6a2 - 19a + 15

(j)

9a2 - 24a + 16

(j)

9a2 -12ab +4b2

Question 7

Factorise (sum and difference of cubes):

I

II

III

(a)

x3 - 8

(a)

y3 - 27

(a)

x3 + 1000

(b)

a3 + 83

(b)

(b)

m3 - 1

(c)

x3 + 1

(c)

8x3 + 125

(c)

64 - 27a3

(d)

216a3 - b3

(d)

x3 + (2y)3

(d)

(e)

(e)

(e)

x3y3 - a3

(f)

(x - 2)3 + 64

(f)

8(a + 1)3 - 1

(f)

27(a - 1)3 - 8

(g)

(x+y)3 - (x-y)3

(g)

(3p + 1)3 - p3

(g)

64(x+1)3 + (2x-3)3


Question 8

Factorise (mixed questions):

I

II

III

(a)

3x2 - 12x

(a)

x3 - x

(a)

2x3 - 8x

(b)

3y2 + 18y + 24

(b)

16 - (3y - 1)2

(b)

2a3 - 16

(c)

50x2 - 72y2

(c)

x2 - 8

(c)

m2n + mn2 -3m - 3n

(d)

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

(d)

ab - 4b + a - 4

(d)

4p2 - 1

(e)

-2x2 - 6x - 4

(e)

3y3 + 24

(e)

a4 - a

(f)

5x3 + 2x2

(f)

x3 - 6x2 + 9x

(f)

2xy + 5x - 2y - 5

(g)

4p - 1) - q(4p - 1)

(g)

12 + 10x - 2x2

(g)

x3y3 + 1

(h)

a2bc + ab2c + abc2

(h)

x2 - 4 + 3(x + 2)

(h)

a2 - b2 + a + b

(i)

4t2 - 8t - 5

(i)

y4 - 1

(i)

x4 - x2y2

(j)

2r2 - 12r - 32

(j)

x6 - 1

(j)

x6 - y6






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