Factoring Practice
I.
Greatest Common Factor (GCF)
Find the GCF of the numbers.
18, 30
· · · · ·
6 = GCF
1.
2.
3.
4.
12, 18
10, 35
8, 30
16, 24
5.
6.
7.
8.
II.
28,
27,
30,
48,
49
63
45
72
Greatest Common Monomial Factor
Factor, write prime if prime.
1.
2.
3.
4.
5.
6.
7.
6 3
24 8
6 12
2 8
4 10
10 35
10 15
! ! !"#
! $
8.
9.
10.
11.
12.
13.
14.
III.
12 9 15
3 12 30
9 4 12
2 3 5
13 26 39
17 34 51
18 12 24 Factoring the Difference of Two Squares
% &% &
' # "' $ %' #&%' #&
Factor, write prime if prime.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
1
9
4
25
9 16
4 25
9 1
25 16 25 12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
– 16
36 121
2 8
25 4 4 81 12 75
98 2 5 45 9 4
16 IV.
Factoring Perfect Square Trinomials
' #' #2 %' 3&
Factor, write prime if prime.
1.
2.
3.
4.
5.
11.
12.
13.
14.
15.
8 16
16 64
12 36
10 25
16 8 1
25 60 36
16 40 25 16 24 9
49 14 1
9 30 25
6.
7.
8.
9.
10.
16.
17.
18.
19.
20.
V.
9 6 1
25 10 1
14 49
81 90 25
4 20 25
2 4
2 1
36 84 49
81 18 4 12 9 Special Factoring – Challenge
Factor, write prime if prime.
1.
2.
3.
4.
5.
6.
36
9 49
169 4(
9) * 25 *
+
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
16
7. 64 ,
8.
100
9.
)
10.
+
.
81
,
VI.
1 8( 16(
6 9
2 4 12 9 100/ 20/ 1
9 24 16
4 8 4
50 200 200 % 4& % 1&
% 1& 10% 1& 25
Factoring Trinomials: x2 + bx + c
' 3' %'& % &' %&%& %' &%' &
Factor, write prime if prime.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
6 8
0 50 6
9 14
10 16
12 27
14 24
15 36
21 54
13 36
8 15
4 32
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
6
3 18
7 18
56
0 40 12
9 36
4 21
22 75
3 40
45 14 13 36
VII.
…More Factoring Trinomials: x2 + bx + c
9 9 %9& %# &9 %#&%& %9 #&%9 &
Factor, write prime if prime.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
7 12
10 21
7 8
6 5
4 32
2 15
6 8
9 18
3 44 4 5 125 20
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
51 206 6 14 24 6 72
11 60 157 278 8 3 21 54 (Hint: Check for GCF)
5 6 8 12 7 10 11 60 VIII. Factoring Trinomials: ax2 + bx + c
' ' %' &%' &
Factor, write prime if prime.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
2 5 3
3 10 8
2 15 7
7 11 4
5 17 6
4 8 3
3 4 7
2 13 15
9 6 8
6 7 20
2 3 14
5 2 7
10 13 30
12 7 1
2 9 5
2 7 6
5 42 27
15 28 32
8 10 3
20. 2 3 20
11.
12.
13.
14.
15.
16.
17.
18.
19.
IX.
…More Factoring Trinomials: ax2 + bx + c
Factor, write prime if prime.
1.
2.
3.
4.
5.
6.
7.
8.
3 4 5) 7) 2
2 11 5
3) ) 2
5/ 2/ 7
88 1084 34 6 19 15
28 5 12 9.
10.
11.
12.
13.
14.
15.
16.
2 7 15 12 17 6
4 4 5 56 15 56
12 29 14
64 32 21
16 56 49
18 57 35
X.
Factoring: Putting It All Together
' ' "' #' $ %' &%' &
Factor Completely, write prime if prime.
1.
2.
3.
4.
5.
6.
7.
8.
2 8
2 8 6
3 9 30
6 26 20
2 12 80
54 154 10
8 18
14 7 21
1.
2.
3.
4.
5.
6.
7.
16 40 24
27 36 12
5 60 140
6 54 6
56 86 46 ,
6 16
9.
10.
11.
12.
13.
14.
15.
16.
XI.
4 16 16
18 12 2 2 2 34 274
24 30 9
10 15 10
3 42 147
4 4 …More Factoring: Putting It All Together
3 4
/ % 6 9&
81 16 4 4 %2 3& % 1&
16: . 8: 1
14. % 4& 4% 4& 4% 4&
8.
9.
10.
11.
12.
13.
XII.
Extra: Factoring by Grouping
' ! #!' ' #!' !
%' & !%' &
%' &% !&
1.
2.
3.
4.
5.
2 2
3 2 6 4 4 4 1 Hint: 4 1 1%4 1&
10 24 58 84
*
0 0 7
6. 4( 5 2(5 2(
7. : 3 : 3:
8.
9.
10.
11.
12.
13.
14.
2 3 6
2 2 ) ) )
4 4
16 16
1
8 8
Factoring Practice Key
I. Greatest Common Factor
1.
2.
3.
4.
5.
6.
7.
8.
6
5
2
8
7
9
15
24
II. Greatest Common Monomial Factor
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
III.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
3%2 1&
8%3 1&
6% 2&
2% 4&
2%2 5&
5%2 7&
5 %2 3 &
3%4 3 5&
3% 4 10&
prime
%2 3 5&
13%1 2 3 &
17% 2 3&
6 %3 2 4&
Factoring the Difference of Two
Squares
% 1&% 1&
% 3&% 3&
prime
% 5&% 5&
%3 4&%3 4&
%2 5&%2 5&
%3 1&%3 1&
% &% &
%5 &%5 &
% 4 &% 4 &
%5 &%5 &
%4 &%4 &
%6 11&%6 11&
2% 2&% 2&
prime
%2 9&%2 9&
3%2 5&%2 5&
% &% &
2%7 &%7 & @7 2% 7&% 7&
5% 3 &% 3 &
%3 2&%3 2&
%4 &%4 &
IV. Factoring Perfect Square Trinomials
1.
2.
3.
4.
5.
6.
7.
% 4&
% 8&
% 6&
% 5&
%4 1&
%3 1&
%5 1&
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
% 7&
%9 5&
%2 5&
%5 6&
%4 5&
%4 3&
%7 1&
%3 5&
prime
% 1&
%6 7&
% 9&
%3 2&
V. Special Factoring – Challenge
% 6&% 6&
%3 7&%3 7&
%13 2(&%13 2(&
% 3) &% 3) &
1.
2.
3.
4.
5.
A 5 BA 5 B
6.
A 4B A 4B
7.
8.
9.
*
*
*
*
%8 &%8 &
% 10&% 10&
-
-
A )B A )B
,
,
% 9&% 3&% 3&
%1 4(& @7 %4( 1&
% 3&
% &
%2 3 &
%10/ 1&
%3 4&
4% 1&
50%20 1&
C% 4& % 1&DC% 4& % 1&D @7 % 5&% 3&
20. C% 1& 5D @7 % 6&
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
VI. Factoring Trinomials: x2 + bx + c
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
% 4&% 2&
%0 2&%0 3&
% 7&% 2&
% 8&% 2&
% 9&% 3&
% 12&% 2&
% 12&% 3&
% 18&% 3&
prime
% 5&% 3&
% 8&% 4&
% 3&% 2&
% 6&% 3&
% 9&% 2&
% 8&% 7&
%0 6&%0 2&
% 12&% 3&
% 7&% 3&
% 25&% 3&
% 8&% 5&
21. % 9&% 5&
22. % 9&% 4&
VII.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
VIII.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
…More Factoring Trinomials: x2 + bx + c
% 4&% 3&
% 3&% 7&
% 8&% 1&
% 1&% 5&
% 8&% 4&
% 5&% 3&
% 2&% 4&
% 3&% 6&
%4 1&%4 3&
%5 2&%5 10&
%3 6&%17 6& @7 %6 3&%6 17&
% 2&% 12&
% 6&% 12&
% 15 &% 4 &
%57 8&%37 8&
3% 2 &% 9 &
% 6 &% &
% 6 &% 2 &
% 5&% 2&
% 15&% 4&
Factoring Trinomials: ax2 + bx + c
%2 1&% 3&
%3 2&% 4&
%2 1&% 7&
%7 4&% 1&
%5 2&% 3&
%2 3&%2 1&
%3 7&% 1&
%2 3&% 5&
%3 2&%3 4&
%3 4&%2 5&
%2 7&% 2&
prime
%2 5&%5 6&
%3 1&%4 1&
%2 1&% 5&
%2 3&% 2&
%5 3&% 9&
%3 8&%5 4&
%2 1&%4 3&
%2 5&% 4&
IX. …More Factoring Trinomials: ax2 + bx + c
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
%3 1&% 1&
%5) 2&%) 1&
%2 1&% 5&
%3) 2&%) 1&
%5/ 7&%/ 1&
%48 34&%28 4&
%2 3&%3 5&
%7 4&%4 3&
%2 3&% 5&
%3 2&%4 3&
prime
%7 8&%8 7&
%4 7 &%3 2 &
%8 7 &%8 3 &
15. %4 7 &
16. %6 5&%3 7&
X. Factoring: Putting It All Together
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
2% 2&% 2&
2% 3&% 1&
3% 5&% 2&
2%3 2&% 5&
2% 10&% 4&
5%4 1&%4 2&
2%2 3&%2 3&
7%2 3&% 1&
4% 2&
2%3 & @7 2% 3&
2%1 &%1 &
34%4 3&%4 3&
3%2 1&%4 3&
5%2 1&% 2&
3% 7&
4 % 1&% 1&
XI. …More Factoring: Putting It All Together
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
XII.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
8%2 1&% 3&
3%3 2&
5% 14&% 2&
6% 9 1&
6 %56 2&%6 2&
% &% &% &
% 8&% 2&
% 1&% 2&% 2&
C/ % 3&DC/ % 3&D @7 %/ 3&%/ 3&
%9 4 &%3 2 &%3 2 &
%2 & @7 % 2&
C%2 3& % 1&DC%2 3& % 1&D @7 %3 2&% 4&
%2: 1& %2: 1&
% 2& % 2&
Extra: Factoring by Grouping
% 2&% &
% 2&%3 &
%4 1&%4 2&
%5 4&%2 8&
%0 7& A 1B
%2( 1&%2( 5&
%: 3&% :&
% 2&% 3&
% &% &%2 &
%) &%) &
% 1&% 2&% 2&
% &% 4&% 4&
% 1& % 1&
% 1&% 8&