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Gautier/Tang
Algebra I: Ch. 5 Part 1
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Date ___________
Section 5-1 Factoring Integers
Prime Number- An integer that is greater than 1 that can only be divided
by 1 and itself.
Examples- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
1. Find the prime factorization of 504.
2 504
2 252
2 126
3
- Divide by prime numbers.
63
= 2 3  32  7
3 21
7
-Answer
2. Find the Greatest Common Factor (GCF) of 882 and 945.
- Find the prime factorization of each integer.
2 882
3 945
3 441
3 315
3 147
3 105
7 49
5 35
7
= 3 2  7  GCF
7
= 63
-Answer
1
Gautier/Tang
Algebra I: Ch. 5 Part 1
Practice Problems
Directions- State whether or not the number is prime. Give the prime
factorization of the number.
1. 31
2. 100
3. 450
4. 98
5. 32
6. 71
7. 132
8. 36
9. 104
10. 39
11. 476
12. 23
Directions- Find the GCF of each pair of numbers.
1. 15 and 25
2. 23 and 46
4. 182 and 196
5. 348 and 426
2
3. 66 and 90
6. 56, 98, 126
Gautier/Tang
Algebra I: Ch. 5 Part 1
Section 5-2 Dividing Monomials
Examples:
1.
15 5

21 7
3.
 4 xy
10 x
-Answer
2.
4.
35 5

42 6
-Answer
c7
c4
 2 xy
5x
- Reduce the fraction.
c7
- Subtract the exponents.
c4
 2y
5
- Cancel out the x’s.
c3
 2y
5
- Answer
5.
b5 b0

 1 -Answer
b5 b0
6.
a3
a8
- Answer
a3
a8
- Subtract the exponents.
1
a5
- The larger exponent is on the bottom, therefore put the exponent
in the denominator and place the a 5 under a 1.
1
a5
- Answer
3
Gautier/Tang
7.
Algebra I: Ch. 5 Part 1
35 x 3 yz 6
56 x 5 yz
5 x 3 yz 6
8 x 5 yz
- Reduce the fraction.
5z 5
8x 2
- Subtract the exponents. Cancel out the y’s.
5z 5
8x 2
- Answer
Practice Problems:
Directions- Divide
1.
24
52
5.
9c 3
3c
9.
12 x 5
 3x 3
2.
10 8
10 5
3.
10 3
10 7
6.
5w 4
15w 2
7.
r 3s 2
rs 4
8.
 6 p3
12 p 5
10.
mn 5
m3n 2
11.
5x 2 y 2
xy
12.
8x 2 y
2 xy
4
4.
6t
2t
Gautier/Tang
Algebra I: Ch. 5 Part 1
Section 5-3 Monomial Factors of Polynomials
Examples:
1.
Divide:
5m  35
5
5m 35

5
5
= m7
-Divide each of the terms on the numerator by 5.
-Answer
2.
3x 4  9 x 3 y  6 x 2 y 2
Divide:
 3x 2
3x 4
9x3 y 6x 2 y 2


 3x 2  3x 2  3x 2
- Divide each of the terms on the numerator by –3x 2 .
=  x 2  3xy  2 y 2
- Answer
Practice Problems
Directions- Divide
1.
7 x  14
7
4.
3c 2 d  12cd 2
3cd
2.
5.
4u  6v
2
3.
2a 3b  6a 2 b 2  4ab 3
2ab
5
6.
14 x  28 y  21z
7
x 2 y 2  x 2 y  xy 2
xy
Gautier/Tang
Algebra I: Ch. 5 Part 1
12 xy  27 y
3y
7.
10.
13.
8.
pq 3  p 3 q
pq
11.
10 z 2  15 z  20
5
9m 5  12m 4  6m 3
 m3
6c 3 d  12cd 3  15cd
3cd
15.
14.
30 p 4 q  45 p 3 q 2  15 p 2 q 3
5 p2q
6
9.
4u 3  10u 2  6u
2u
12.
x 2 y  xy 2  xy
xy
28r 3 s 2  42r 2 s 3  56r 3 s 3
 7r 2 s 2