1. Chapter 3
Factoring

2. 1. Write the prime factorization of 630.2
315 5 63 3 21 3 7
= 2 x 32 x 5 x 7

3. 2. Determine the greatest common factor of 56 and 88.1,
2, ,
4, ,
7, 8, 88 1,
2, ,
4, ,
8, 11,

4. 2. Determine the greatest common factor of 56 and 88.28 2 44 2 14 2 22 2 7 2 11
GCF = 2x2x2
= 8

5. 3. Determine the least common multiple of 10 and 22.
40,
50,
60,
70,
80,
90,
100,
110,
120,
10,
20,
30, 22
22,
44,
66,
88,
110,
132,
154,
176,
198,
220,
240

6. 3. Determine the least common multiple of 10 and 22.5 2 11
= 2 x 5
= 2 x 11
Circle prime factors so the highest power of each prime is selected, then multiply those to find LCM
LCM = 2x5x11
LCM = 110

7. 4. Determine the edge length of this cube.
V = (x)(x)(x)
91125 = x3
x = 45 cm

8. 5. Factor the binomial 6. Factor the trinomial = 11a( 4 + 9a) = -8cd(

9. 7. Expand and simplify: 8. Expand and simplify: = 25m2 – 15mn – 15mn
= 56h3
– 32h2
+ 8h
+21h2
– 12h +3
= 56h3
– 11h2
– 4h +3

10. 9. Expand and simplify: = 10x4 – 4x3 + 6x2 + 25x3 – 10x2 + 15x – 30x2
– 18
= 10x4
+21x3
– 34x2
+ 27x
– 18

11. 10. Expand and simplify: = (18x2 + 48xy – 3xy – 8y2) – ( 4x2 – 6xy
= (18x2 + 45xy – 8y2)
– (4x2 – 12xy +9y2)
= 14x2
+ 57xy
– 17y2

12. 11. Factor the following: a) = (x )(x ) + 6 – 2 No Step 1 -12 2 3 4 5
Is there a common factor?
Step 1 No
-12
Multiply (+1)(-12) 2
Look for numbers:
___ x ___ -12
___ + ___ +4 3
= (x )(x )
+ 6
– 2
+6 & -2 4
Split into Brackets. First coefficient is always the same as original expression.
Divide by the GCF in each bracket 5

13. 11. Factor the following: b) = (9c )(9c ) – 6 – 6 3 3 = (3c– 2)
Is there a common factor?
Step 1 No
+36
Multiply (+9)(+4) 2
Look for numbers:
___ x ___ +36
___ + ___ -12 3
= (9c )(9c )
– 6
– 6 3 3
-6 & -6
(3c– 2) 4
Split into Brackets. First coefficient is always the same as original expression.
= (3c– 2)
= (3c– 2)2
Divide by the GCF in each bracket 5

14. 11. Factor the following: c) = 2( 12b2 + 25b – 7) = 2(12b )(12b ) + 28
Is there a common factor?
Step 1
Yes
Multiply (+12)(-7) 2
-84
Look for numbers:
___ x ___ -84
___ + ___ +25 3
= 2(
12b2 + 25b – 7)
+28 & -3
= 2(12b )(12b )
+ 28
– 3 4 3 4
Split into Brackets. First coefficient is always the same as original expression.
=2(3b + 7)
(4b – 1)
Divide by the GCF in each bracket 5

15. 11. Factor the following: d) = (7s 8t)(7s 8t) + –
Is there a common factor?
Step 1 No
Difference of Squares
Take the square root of both terms and separate into two sets of brackets. 2
= (7s 8t)(7s 8t) + –
One Positive and One Negative 3

16. 11. Factor the following: e) = (8c d)(8c d) + 20 – 2 4 2 =(2c + 5d)
Is there a common factor?
Step 1 No
-40
Multiply (+8)(-5) 2
= (8c d)(8c d)
+ 20
– 2
Look for numbers:
___ x ___ -40
___ + ___ +18 3 4 2
+20 & -2
=(2c + 5d)
(4c – d) 4
Split into Brackets. First coefficient is always the same as original expression.
Divide by the GCF in each bracket 5

17. 11. Factor the following: f) = 3z2( z2 – 256) = 3z2(z 16)(z 16) + –
Is there a common factor?
Step 1
Yes
Difference of Squares
Take the square root of both terms and separate into two sets of brackets. 2
= 3z2( z2
– 256)
One Positive and One Negative 3
= 3z2(z )(z ) –

18. 12. Calculate the area of the shaded region
Large Rectangle:
= 6x2
– 2x
+ 9x
– 3
= 6x2 + 7x – 3
Small Rectangle:
AShaded = (6x2 + 7x – 3)
– (2x2 – x)
= 4x2
+ 8x
– 3
= 2x2
– x

19. Algebra Tiles
+x2
-x2 -x +x -x +x -1 +1

20. 13. Draw the following factors using algebra tiles
13. Draw the following factors using algebra tiles. There is a legend on your formula sheet: a) +6
This is the number of small tiles
Step 1: Factor
= (x + 3)(x + 2)
This is the number of big tiles
Represents the long skinny tiles
(x + 3)
(x + 2)

21. 13. Draw the following factors using algebra tiles
13. Draw the following factors using algebra tiles. There is a legend on your formula sheet: b)
This is the number of small tiles +2
Step 1: Factor
= (x – 2)(x – 1)
This is the number of big tiles
Represents the long skinny tiles
(x – 2)
(x – 1)

22. 13. Draw the following factors using algebra tiles
13. Draw the following factors using algebra tiles. There is a legend on your formula sheet: c)
This is the number of small tiles
-12
Step 1: Factor
__ x __ = -12
__+__ = +1
= (2x + 4)(2x – 3)
This is the number of big tiles 2 1
(2x – 3)
= (x + 2)(2x – 3)
Represents the long skinny tiles
(x + 2)

23. 13. Draw the following factors using algebra tiles
13. Draw the following factors using algebra tiles. There is a legend on your formula sheet: d)
This is the number of small tiles -3
Step 1: Factor
__ x __ = -3
__+__ = -2
= (x + 1)(x – 3)
This is the number of big tiles
(x – 3)
Represents the long skinny tiles
(x + 1)