Name _____________________________________________ Period ____
Factoring Unit
Day 1
Multiplying Binomials
1) (2n+ 2)(6n+ 1)
2) (4n+ 1)(2n+ 6)
3) ( x− 3)(6 x− 2)
4) (8 p− 2)(6 p+ 2)
12n2+14n+2
8n2+26n +6
6x2-20x+6
48p2+4p-4
5) (6 p+ 8)(5 p− 8)
6) (3m− 1)(8m+ 7)
7) (2a− 1)(8a− 5)
8) (5n+ 6)(5n− 5)
30p2 -8p -64
24m2 +13m -7
16a2 -18a+5
25n2 + 5n -30
9) (4 p− 1)2
10) (7 x− 6)(5 x+ 6)
11) (6n+ 3)(6n− 4)
12) (8n+ 1)(6n− 3)
16p2 -8p + 1
35x2 +12x -36
36n2 -6n -12
48n2 -18n -3
13) (6k+ 5)(5k+ 5)
14) (3 x− 4)(4 x+ 3)
30k2 +55k + 25
12x2 -7x -12
Day 2
Find GCF
1. x2 – 5x
2. 3x – 12
3. 2 x2 + 12x
x(x-5)
3(x-4)
2x(x+6)
4. x2 + 3x
5. 4x3 + 4x
6. 6a2 b – 2ab2
x(x+3)
4x(x2 +1)
2ab(3a – b)
7. 8ax – 56a
8. x3 – 2x2
9. 3x2 – 12x
8a(x-7)
x2(x-2)
3x(x-4)
10. 81 – 36xy
11. t2h + 3t
12. 5c3 – 2c2
9(9 – 4xy)
t(th + 3)
c2(5c – 2)
13. 36xy2 – 48x2y
14. 75b2c3 + 60bc6
15. 6e3f – 11ef
12xy(3y-4x)
15bc3(5b +4c3)
ef(6e2 -11)
16. 20p2 – 16p2 q2
17. 34x4y3 – 17x2y5
18. 35m3n + 105m2n3
4p2(5-4q2)
17x2y3(2x2 – y2)
35m2n(m + 3n2)
Day 3
Factor by grouping
1. 8r3 - 64r2 + r – 8
2. 12p3 – 21p2 + 28p – 49
3. 12x3 + 2x2 – 30x – 5
(8r2+1)(r-8)
(3p2+7)(4p-7)
(2x2-5)(6x+1)
4. 6v3 – 16v2 + 21v – 56
5. 63n3 + 54n2 – 105n – 90
6. 21k3 – 84k2 + 15k – 60
(2v2+7)(3v-8)
3(3n2-5)(7n+6)
3(7k2+5)(k-4)
7. 25v3 + 5v2 + 30v + 6
8. 105n3 + 175n2 – 75n – 125
9. 96j3 – 84j2 + 112j – 98
(5v2+6)(5v+1)
5(7n2-5)(3n+5)
2(6j2+7)(8j-7)
10. 28r3 + 16r2 - 21r – 12
11. 4v3 – 12v2 – 5v + 15
12. 49x3 – 35x2 + 56x – 40
(4r2-3)(7r+4)
(4v2-5)(v-3)
(7x2+8)(7x-5)
13. 24p3 + 15p2 – 56p – 35
14. 24r3 - 64r2 – 21r + 56
(3p2-7)(8p+5)
(8r2-7)(3r-8)
Day 4
Factoring a=1, a>1, and difference of 2 squares
1. x2 + 8x +16
2. x2 - 7x + 10
3. x2 + 32x – 144
4. x2 – x – 12
(x+4)(x+4)
(x-5)(x-2)
(x-4)(x+36)
(x-4)(x+3)
2
5. x – 13x + 40
6. x + 8x – 20
7. x – 10x +25
8. x2 + 6x – 16
(x-8)(x-5)
(x+10)(x-2)
(x-5)(x-5)
(x+8)(x-2)
9. x2 + 2x – 3
10. x2 + 12x + 36
11. x2 – 18x + 81
12. x2 + 16x + 64
(x+3)(x-1)
(x+6)(x+6)
(x-9)(x-9)
(x+8)(x+8)
13. x2 – 10x + 25
14. x2 + 10x + 25
15. x2 - 14x + 49
16. x2 – 6x + 9
(x-5)(x-5)
(x+5)(x+5)
(x-7)(x-7)
(x-3)(x-3)
17. x2 – 4x + 4
18. x2 – 9
19. x2 – 36
20. 16x2 – 1
(x-2)(x-2)
(x+3)(x-3)
(x-6)(x+6)
(4x+1)(4x-1)
21. 49x2 – 1
22. 9x2 – 16
23. x2 – y2
24. 4x2 – 36
(7x-1)(7x+1)
(3x-4)(3x+4)
(x-y)(x+y)
2
2
2
25. 36x – 49
26. 9 – x
(6x-7)(6x+7)
(3-x)(3+x)
2
2
2
4
(2x-6)(2x+6)
27. 625y – 16z
28. 2x2 – 32
(25y2+4z2) (25y2-4z2)
2(x-4)(x+4)
2
4
29. 2x + 5x – 12
30. 6x -13x – 28
31. 3x - 23x +30
32. 10 x2 – 42x +4
(2x-3)(x+4)
(2x-7)(3x+4)
(x-6)(3x-5)
can’t be factored
33. 4x2 - 8x +3
34. 6x2 + 19x +10
35. 6x2 + 5x +1
36. 4x2 + 4x – 3
(2x-3)(2x-1)
(3x+2)(2x+5)
(3x+1)(2x+1)
(2x-1)(2x+3)
37. 3x3 – 9x2 – 30x
38. 5x3 + 30x2 + 45x
39. 2x2 + 8x – 10
40. 3x2 + 24x + 48
3x(x-5)(x+2)
5x(x+3)(x+3)
2(x+5)(x-1)
3(x+4)(x+4)
Day 5
Factoring to Solve
1) (3n− 2)(4n+ 1)= 0
2) m(m− 3)= 0
3) (5n− 1)(n+ 1)= 0
4) (n+ 2)(2n+ 5)= 0
n= 2/3 or -1/4
m= 0 or 3
n= -1 or 1/5
n = -2 or -5/2
5) 3k2+ 72 = 33k
6) n2= −18 − 9n
7) 7v2− 42 = −35v
8) k2= −4k− 4
k= 3 or 8
n= -6 or -3
v= -6 or 1
k = -2
9) −2v2− v+ 12 = −3v2+ 6v
10) −4n2+ 6n− 16 = −5n2
11) 8r2+ 3r+ 2 = 7r2
12) b2+ b= 2
v= 4 or 3
n= -8 or 2
r= -2 or -1
b= -2 or 1
13) 2x2 + 13x + 21 = 0
14) 20x2 - 6x - 8 = 0
15) 14x2 - 45x - 14 = 0 16) 10x2 + 24x + 14 = 0
x= -7/2 or -3
x= -1/2 or 4/5
x= 7/2 or -2/7
17) - 28x2 + 3x + 18 = 0
18) - 21x2 - 8x + 5 = 0
19) - 6x2 + 15x - 9 = 020) 28x2 - 54x + 18 = 0
x= -3/4 or 6/7
x= -5/7 or 1/3
x= 3/2 or 1
Day 6
Simplifying Radicals
x= -1 or -7/5
x= 3/2 or 3/7
Simplify each expression if it represents a real number. Use imaginary numbers when
necessary.
1. 16
2.  16
3. 64
4. 64
5. 81
4
-4
8
8i
9
6. 81
7. 72
8. 56
9. 300
10. 24
9i
6√2
2√14
10√3
2i√6
11. 48
12. 27
13.  8
14. 75
15.  108
4i√3
3i√3
-2i√2
5√3
-6√3
16.  54
17. 48
18.  98
19. 150
20. 252
-3i√6
4√3
-7√2
5√6
6√7
21. 40
22.  20
23. 18
24.  16
25. 288
2√10
-2i√5
3√2
-4i
12√2
26.  500
27. 180
28. 176
-10√5
6i√5
4√11