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Name ________________________________________ Date __________________ Class__________________
LESSON
8-1
Review for Mastery
Factors and Greatest Common Factors
A prime number has exactly two factors, itself and 1. The number 1 is not a prime number.
To write the prime factorization of a number, factor the number into its prime factors only.
Find the prime factorization of 30.
The prime factorization of 30 is 2 • 3 • 5.
Find the prime factorization of 84.
The prime factorization of 84 is 2 • 2 • 3 • 7 or 22 • 3 • 7.
Fill in the blanks below to find the prime factorization of the given
numbers.
1.
2.
________________________
3.
________________________
________________________
Write the prime factorization of each number.
4. 99
________________________
5. 75
6. 84
_________________________
________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
8-6
Holt McDougal Algebra 1
Name ________________________________________ Date __________________ Class__________________
LESSON
8-1
Review for Mastery
Factors and Greatest Common Factors continued
If two numbers have the same factors, the numbers have common factors.
The largest of the common factors is called the greatest common factor, or GCF.
Find the GCF of 12 and 18.
Think of the numbers you multiply to equal 12.
1 × 12 = 12
2 × 6 = 12
The factors of 12 are: 1, 2, 3, 4, 6, 12
3 × 4 = 12
Think of the numbers you multiply to equal 18.
1 × 18 = 18
2 × 9 = 18
The factors of 18 are: 1, 2, 3, 6, 9, 18.
3 × 6 = 18
The GCF of 12 and 18 is 6.
Find the GCF of 8x2 and 10x.
The factors of 8x2 are: 1, 2, 4, 8,
x, x
The factors of 10x are: 1, 2, 5, 10, x
2
x
2
The GCF of 8x and 10x is 2x.
Find the GCF of 28 and 44 by following the steps below.
7. Find the factors of 28.
_____________________________________
8. Find the factors of 44.
_____________________________________
9. Find the GCF of 28 and 44.
_____________________________________
Find the GCF of each pair of numbers.
10. 15 and 20
________________________
11. 16 and 28
________________________
12. 24 and 60
________________________
Find the GCF of each pair of monomials.
13. 4a and 10a
________________________
14. 15x3 and 21x2
________________________
15. 5y2 and 8y
________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
8-7
Holt McDougal Algebra 1
Problem Solving
1. x 2 − 16; $128
2. 0.75x 2 − x − 65; 2575 square feet
3. x 2 − 144 in2
4. D
5. G
6. A
5. 24 i 32
6. 32 i 17
7. 4
8. 9
9. 1
10. 7
11. 33
12. 20
13. 6
14. 42
15. 5x
7. G
2
16. 6
17. 3t
18. 9y
19. 12
20. 2d3
1. difference of squares
21. m6n
22. 5h
2. perfect square trinomial
23. a. 16
Reading Strategies
b. 4
3. It will have 3 terms.
4. c 4 + 20c 2 d + 100d 2 ;
perfect square trinomial
Practice C
2
5. 4s − 9; difference of squares
LESSON 8–1
Practice A
1.
32 i 2 2
1. 3 i 52
2. 25 i 5
3. 22 i 53 i 7
4. 18
5. 6
6. 1
7. 18
8. 6
9. 4
10. 1
11. 8
12. 7m
13. 13
14. 4x2y
15. 6s3t 4
16. 6
17. x
2.
2
19. 7y
18. 1
2
20. 5 baskets; each will have 6 oranges,
9 apples, and 4 pears.
21. There will be 25 rows with 3 vehicles in
each row. There will be 12 rows of cars,
4 rows of vans, and 9 rows of trucks.
3.
Review for Mastery
1.
53
4. 5
5. 8
6. 12
7. 25
8. 3y2
9. p
10. 6
11. 7y
12. 16
13. 7
22 i 11
2.
2
Practice B
1. 2 i 32
2. 23 i 3 i 5
3. 23 i 7
4. 2 i 3 i 5 i 13
23 i 7
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A12
Holt McDougal Algebra 1
3.
LESSON 8–2
Practice A
4
3
2
2
4. 3 i 11
5. 3 i 5
2
6. 2 i 3 i 7
7. 1, 2, 4, 7, 14, 28
8. 1, 2, 4, 11, 22, 44
9. 4
10. 5
11. 4
12. 12
13. 2a
14. 3x2
15. y
1. 3 5 11
1
10
2. 5; m3
3. 5; y5; 2
4. 2y2(5 + 6y)
5. 6t(2t 4 + 1)
6. 3x2 (2x 2 + 5x +1)
7. 5t(t + 8)
8. 3x and x + 8
9. (d + 2)(4d + 9)
10. (x 5)(12 + 7x)
11. 3n 2 ; 12; 3; 3; (n + 3)(n2 + 4)
12. (2x + 5)(x2 + 1)
13. 2y3; 6; y; 2; y; y; y; 2; (y 2)(2y2 3)
Challenge
1 2
1. x; 5
14. (m 3)(4m2 5)
2 2 1
2. 3 5 7
Practice B
3. 2
4. 24325271
5. 2, 3, 5, and 7
6. 2 and 11
1. c(8c + 7)
2. 3n2(n + 4)
7. relatively prime
8. 3, 5, 17, and 31
3. 3x(5x 4 6)
4. 4(2s 4 + 5t3 7)
10. 21112
5. 6n(n 5 + 3n3 4)
11. 1
12. 3255172315
6. 5m2 (m 2 m + 1)
13. 233471
14. 1
7. 16t(t + 2)
9. 21325272
8. 3x and 4x + 1
Problem Solving
9. (m + 5)(3m + 4)
1. 9 awards in each row; total of 5 rows
2
10. (b 3)(16b + 1)
11. (x + 4)(2x + 3)
12. (4n + 3)(n2 + 1)
13. (5d 3)(2d + 7)
14. (4n 5)(3n2 2)
3. 8 centerpieces; 9 carnations,
10 lilies, 8 rosebuds
15. (b 3)(5b3 1)
16. (t2 2)(t 5)
4. 6 rows
5. A
Practice C
6. H
7. D
2. 12 snacks of 4 carrot sticks and
3 apple slices
Reading Strategies
1. 4x2 (2x 2 3)
2. 4b(3ab 2 + 5)
3. 2(8m 2 n3 + 15m)
4. 9j(3j 3 8j2 + 1)
1. 1, 2, 4, 7, 14, 28
2. a i a i a i a i a
5. 5x3(x 2 7x + 6)
3. 1, 2, 4, 8, 16
4. a i a
6. 16x2y(x 4 + y3 + 2xy)
7. 2r(r + h)
1
8.
x and 3x + 1
2
9. (k 2)(10 + 7k)
6. 2m
5. 4a2
7. no; 11 and 3 are factors.
8. 2 i 33
9. 2 i 3 i 52
4
10. 2 i 5
11. (t + 3)(2t2 + 1)
10. (m + 7)(9m2 + 5)
12. (3n + 2)(n3 5)
13. (6a 7)(2a + 5)
14. (2n2 + 1)(5n3 14)
15. (3b3 1)(b 8)
16. (x 4)(3x2 5)
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A13
Holt McDougal Algebra 1