TEACHER MANUAL ALGEBRA II / LESSON 11
Answers:
1. y4 x3 v + 14 = 8
2. 2x + 6 = 1
3. 5y10 – 6x7y3 – 4y – 5 = 10
4. x3 +4y - 9 = 3
5. 60x2 y + 8 = 3
6. 5y3 – 4y – 1 = 3
7. 4x4 y3 + v y + 7 = 7
8. 8n5 – 4n2 – x = 5
9. 134x10 y3 + x2 v y + 7 = 13
10. 1,234u15 v12 w10x8y6 z4 + 4 = 55
For problems 11-15 determine the leading term, leading coefficient, and constant term of each polynomial
11. 5y3 – 4y – 1
Leading term: 5y3 Leading coefficient: 5 Constant term: -1
12. 4x4 y3 + v y + 7
Leading term: 4x4 y3 Leading coefficient: 4 Constant term: 7
TEACHER MANUAL ALGEBRA II / LESSON 11
13. 8n5 – 4n2 – 2
Leading term: 8n5 Leading coefficient: 8 Constant term: -2
14. 134x10 y3 + x2 v y + 123
Leading term: 134x10 y3 Leading coefficient: 134 Constant term: 123
15. 1,234u15 v12 w10x8y6 z4 + 4
Leading term: 1,234u15 v12 w10x8y6 z4 Leading coefficient: 1,234 Constant term: 4
16. x8y + x4y + 2 no
17. y2 + 4y + 16 yes/(y + 4) 2
18. 9y2 + 6y + 1 yes/(3y + 1) 2
19. x2+ 16 no
20. x4 + 12x2+ 36 yes/(x2+ 6) 2
Lesson Wrap up: Please review the answers for the problems from the lesson for today with the student. Go over the answers so that they may see which problems they got correct and incorrect. Have the student review and redo any incorrect answers to the problems given in today’s lesson.
TEACHER MANUAL ALGEBRA II / LESSON 12
Answers:
1. (10b8 + 3ab7 + c + 9abc + 4b2) + (1 + c + 4ab7 + 9b2)
= 10b8 + 7ab7 + 2c + 9abc + 13b2 + 1
2. (13yx7 + 11yz9 + x + 9 + 8xy2) + (yz9 + 13xy7 + x + 10 + xy2)
= 26xy7+ 12yz9 + 2x + 19 + 9xy2
3. (5 + n + 4mo2 + 8n8) + (19 + 16mo2 + 4n10 + 9mno2) + (45 + n)
= 69 + 2n + 20mo2+ 8n8+ 4n10+ 9mno2
4. (15yz3 + 13xy7 + x + 9 + 4x2) + (1 + x + 4xy7 + 8yz3)
= 23yz3+ 17xy7 + 2x + 10 + 4x2
5. (9ab7 + bc + 14ab3 + 9a + 4ab2) + (1 + a + 16ab3+ 4ab7 +bc + 9ab2)
= 13ab7+ 2bc + 30ab3 + 10a + 13ab2 + 1
6. (12 + r + 6s4t2 + 8st2) + (19 + 16s2 + 4st7 + 6s4t2 + st2) + (8s4t2 + 15 + r)
= 46 + 2r + 20s4t2+ 8st2 + 16s2 + 4st7
7. (3xy2+ 6yx5 + 11yz9 + y + 87) + (13yx5 + 13xy2 + y + 10 + yx5)
=16xy2 + 20yx5+ 11yz9 + 2y +97
8. (n2 + 4 + 4o3 + n) + (4 + n + 4m2n2 + 8n2) + (18 + 9m2n2 + 4o3 + 9n2)
= 18n2 + 26 + 4o3 + 2n + 13m2n2
TEACHER MANUAL ALGEBRA II / LESSON 12
9. (12 +6s4t2 +s) + (10 + s + 6s4t2 + 8s2) + (21+ 6s4t2 + 7s4t2)
= 43 + 25s4t2 + 2s + 8s2
10. (13yx5) + (13xy2 + 19y + 3z9) + (x + yz9+ 8xy5) + (yz9 + 43xy2 + 11y + 6z9+ xy2)
= 21yx5 + 57xy2 + 30y + 9z9 + x + 2yz9
21. (10b8 + 3ab7 + c + 9abc + 4b2) + (1 + c + 4ab7 + 9b2)
= 10b8 + 7ab7 + 2c + 9abc + 13b2 + 1 = 10b8 + 7ab7 + 9abc + 13b2 + 2c + 1
22. (13yx7 + 11yz9 + x + 9 + 8xy2) + (yz9 + 13xy7 + x + 10 + xy2)
= 26xy7+ 12yz9 + 2x + 19 + 9xy2 = 12yz9 + 26xy7+ 9xy2+ 2x + 19
23. (5 + n + 4mo2 + 8n8) + (19 + 16mo2 + 4n10 + 9mno2) + (45 + n)
= 69 + 2n + 20mo2+ 8n8+ 4n10+ 9mno2 = 4n10+ 8n8+ 9mno2+ 20mo2 + 2n + 69
24. (15yz3 + 13xy7 + x + 9 + 4x2) + (1 + x + 4xy7 + 8yz3)
= 23yz3+ 17xy7 + 2x + 10 + 4x2 = 17xy7+ 23yz3 + 4x2 + 2x + 10
25. (9ab7 + bc + 14ab3 + 9a + 4ab2) + (1 + a + 16ab3+ 4ab7 +bc + 9ab2)
= 13ab7+ 2bc + 30ab3 + 10a + 13ab2 + 1 = 13ab7+ 30ab3 ++ 13ab2+ 2bc + 10a + 1
26. (12 + r + 6s4t2 + 8st2) + (19 + 16s2 + 4st7 + 6s4t2 + st2) + (8s4t2 + 15 + r)
= 46 + 2r + 20s4t2+ 8st2 + 16s2 + 4st7 = 4st7 + 20s4t2 + + 8st2 + 16s2 + 2r + 46
27. (3xy2+ 6yx5 + 11yz9 + y + 87) + (13yx5 + 13xy2 + y + 10 + yx5)
=16xy2 + 20yx5+ 11yz9 + 2y +97 = 11yz9 + 20yx5 +16xy2 + 2y + 97
TEACHER MANUAL ALGEBRA II / LESSON 12
28. (n2 + 4 + 4o3 + n) + (4 + n + 4m2n2 + 8n2) + (18 + 9m2n2 + 4o3 + 9n2)
= 18n2 + 26 + 4o3 + 2n + 13m2n2 = 13m2n2 + 4o3 + 18n2 + 26 + 2n
29. (12 +6s4t2 +s) + (10 + s + 6s4t2 + 8s2) + (21+ 6s4t2 + 7s4t2)
= 43 + 25s4t2 + 2s + 8s2 = 25s4t2 + 8s2 + 2s + 43
30. (13yx5) + (13xy2 + 19y + 3z9) + (x + yz9+ 8xy5) + (yz9 + 43xy2 + 11y + 6z9+ xy2)
= 21yx5 + 57xy2 + 30y + 9z9 + x + 2yz9 = 2yz9 + 9z9 + 21yx5 + 57xy2 + 30y + x
Lesson Wrap up: Please review the answers for the problems from the lesson for today with the student. Go over the answers so that they may see which problems they got correct and incorrect. Have the student review and redo any incorrect answers to the problems given in today’s lesson.
TEACHER MANUAL ALGEBRA II / LESSON 13
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Answers:
1. (10b2 + 3abc + c) - (abc + 4b2)
TEACHER MANUAL ALGEBRA II / LESSON 13
= 2abc + 6b2 + c
2. (7yx7 + 11y - 8xy2) - (yz9 + 17xy7 - xy2)
= -yz9 -10yx7 - 7xy2 + 11y
3. (34 + n - 4mo2 - 8n8) - (16 + 16mo2 + 12mno2) - (16 + n)
= - 8n8 - 12mno2- 20mo2 + 66
4. (- 23xy7 + x + 9 + 8z3) - (5 + 6x) - (7xy7 + 8z3)
= - 30xy7 - 5x + 4
5. (4ab7 - 22ab3 + 3a - 4ab2) - (19 + 3a + 16ab3+ 4ab7 - 9ab2)
= - 38ab3 + 5ab2 - 19
6. (172 - r + 9s4t2 + 8st2) - (21st7 + 6s4t2 + 8st2) - (8s4t2 + 10 - 5r)
= - 21st7 - 5s4t2 + 6r +162
7. (7xy2+ 9yx5 + 7y + 13) - (13yx5 - 93xy2 + 8y - 17 + yx5)
= - 5yx5 + 100xy2 – y + 30
8. (m2 + 14 - 4o3 + m) - (14 + m + 14m2n2 + 8m2) - (14 + 14m2n2 - 4o3 + 4m2)
= -11m2 - 14
9. (21+ 14s4t2 - 7s4t2) - (t2 +5s4t2 +s) - (10 t2 - 6s4t2 + 7s2)
= 8s4t2 - 11t2 - 7s2 –s + 21
10. (x - z9+ 2xy2) - (8z9 + 43xy2 - 16y + 10z9+ 3xy2) - (3yx5) - (13xy2 - 19y + 3z9)
= - 22z9x - 3yx5 - 25xy2 + 3y
TEACHER MANUAL ALGEBRA II / LESSON 13
11. (x + 3) 2 - (x - 4) 2
= 14x + 25
12. (2y - 5) 2 - (y + 6) 2
= 3y 2 - 32y – 9
13. (3m - 4) 2 - (m + 4)2
= 8m 2 - 32m –32
14. (7b2 - 7) 2 - (2b2 - 11) 2
= 53b 4 - 142b 2 + 170
15. (5ab2 + 3) 2 - (6ab2 - 7) 2
= -9a2b 4 + 114ab 2 + 58
Answers for 16 – 20 will vary. Please double-check for correctness.
Lesson Wrap up: Please review the answers for the problems from the lesson for today with the student. Go over the answers so that they may see which problems they got correct and incorrect. Have the student review and redo any incorrect answers to the problems given in today’s lesson. Also, be sure to review the problems that the student wrote his or her self in today’s lesson for correctness.
TEACHER MANUAL ALGEBRA II / LESSON 14
Answers:
1. (5xy + 6) (7xy2 + 8)
= 35x2y3 + 42xy2 + 40 + 48
2. (4y + y2) (7xy2 + 6)
= 7x2y3+ 28x2y + 6y2+ 24y
3. (ab + 2b2) (5b2 + 3ab)
= 5b4+ 5a2b2+ 3a2b2 +6ab3
4. (9xyz + 3xy2) (xy2 + 6)
= 9x2y2z + 3x2y2 + 18xyz+ 18xy2
5. (4b + 2b2) (5b2 + 3b)
= 10b4 +26b3 +12b2
6. (7yx7 + 11)(yz9 - 17xy4 + xy2)
= 7y2x7 z9 - 119x8y5 +7x8y3 +11yz9 – 187xy4 -11xy2
7. (4mo2 - 8n2) (16mo2 + 12mno2 – 5m)
= 48m2no4 + 64m2o4 -96mn3o2 +20m3o2– 128n2mo2 +4mn2
8. (- 3xy7 + y) (3 + 2z3 – 17)
TEACHER MANUAL ALGEBRA II / LESSON 14
= -6xy7 z3 - 60xy7 +2yz3 -14y
9. (3ab5 - 12ab3) (7a - 4ab2 – 18)
= 12a2b7+ 69a2b5 -54ab5 - 84a2b3+ 192ab3
10. (3a + 15ab3) (5ab7 - 3ab2- 5)
= 75a2b10+ 15a2b7 - 45 a2b5-9a2b2 - 75ab3 - 15a
11. (5r + 6s4t2 - 4st2)(2st5 + 8s4t2 - 4st2)
= 12s5t7+ 48s8t4 - 24s5t4 – 32s5t4 - 8s2t6 –10rst5 – 40rs4t2 – 16s2t4–40rst2
12. (4xy2+ 4y + 14) (14yx4 + 4xy2 + 8y)
= 56x5y3 + 48xy6 + 16x2y4 +56y2x4 +196yx4 + 56xy2 + 32y2 + 112y
13. (5m2n2 + 5o3 + m)(5m2n2 + 5m2 + 5m)
= 25m2n2o3 + 25m4n2 + 50m3n2 +5m3n2 + 5m3 +5m2
14. (14s4t2 - 7s4t2 + 12) (t2 +6s4t2 +s)
= 42s8t4+ 12s4t4 + 7s5t2 + 72s4t2 + 12t2 +12s
15. (3xy2 + 2xy2+8z2) (4xy2 - 16y + 10z2)
= 20x2y4 + 82xy2 z2 + 80z2 - 80xy3 - 128yz2
TEACHER MANUAL ALGEBRA II / LESSON 14
Answers for 16 – 20 will vary. Please double-check for correctness.
Lesson Wrap up: Please review the answers for the problems from the lesson for today with the student. Go over the answers so that they may see which problems they got correct and incorrect. Have the student review and redo any incorrect answers to the problems given in today’s lesson. Also, be sure to review the problems that the student wrote his or her self in today’s lesson for correctness. Make sure that the student is clearly writing out all the steps to their process for finding the solution, that way, you can easily go back through their work to see where they may have made simple errors.
TEACHER MANUAL ALGEBRA II / LESSON 15
Answers:
1. 5xy +10xy2 + 5x = 5x
2. 4y + xy2 + 6y = y
3. ab + 2a2b2 + 3ab = ab
4. 9xyz + 3xy4z+ 3xy2 + 6xz = 3x
5. 4ab + 5ba2 + 3b = b
6. 2yx7 + 10yz9 + xy4 + 5xy2 = xy
7. 4mn7o2 + 8n2o+ 16mn3o2 + 12mn3o2 – 20mn2 o = 4n2o
8. - 3xy7z + xyz3 + 2xyz3 + z= z
9. 2ab5 - 12ab3 + 4ab2 + 18 b2 = 2b2
10.3ab5 + 15ab3 + 5ab2 - 3ab2- 5b) = b
11.6s4t2 +10st - 4st2 ÷ 2st = 5 + 3s3t - 2t
12.4xy2+ 4xy4 + 12xy2 ÷ 4xy2 =y2 + 3y
13.5m2n2 + 5mno3 + 5mno2 ÷ 5mn = mn+ o3 + o2
14.14s4t2 - 7s4t2 + 12t2 ÷ t = 14s4t - 7s4t + 12t
15.12xy5 + 24xy4 + 8xy3 ÷ 4xy2 =3y3 + 6y2 + 2y
16.20yx7 + 10xyz6 + xy4 + 30xy2 ÷ 2xy = 20yx7 + 10xyz6 + xy4 + 30xy2
17.4mn7o2 - 16mn3o2 + 12mn3o + 8mn2o ÷ 4mn2 o =n5o - 4no + 3n + 2
18.- 3xy7z + xyz3 + 2xyz ÷ yz = -3xy6 + xz2 + 2x
19.84ab5 - 12ab3 + 4ab2 + 18b2 ÷2b2 = 42ab3 - 6ab + 2a + 9
20.30ab5 + 15ab3 + 5ab2 - 105ab2- 75ab ÷ 5ab = 6b4 + 3ab2 + b - 21b- 15
Lesson Wrap up: Please review the answers for the problems from the lesson for today with the student. Go over the answers so that they may see which problems they got correct and incorrect. Have the student review and redo any incorrect answers to the problems given in today’s lesson. Also, be sure to review the problems that the student wrote his or her self in today’s lesson for correctness. Make sure that the student is clearly writing out all the steps to their process for finding the solution, that way, you can easily go back through their work to see where they may have made simple errors.
TEACHER MANUAL ALGEBRA II / LESSON 16
Answers:
1. (x2 + 2x -15) ÷ (x -3) = (x +5)
2. (a2 - a -30) ÷ (a - 6) = (a +5)
3. (b2 - 6 + 9) ÷ (b -3) = (b - 3)
4. (2y2 – 9y + 10) ÷ (y -2) = (2y +5)
5. (2m2 – 3m - 9) ÷ (m + 3) = (2m - 3)
6. (4a2 + 22a - 12) ÷ (a + 6) = (4a - 2)
7. (x3 + 4x3 + x -6) ÷ (x + 2) = (x2 + 2x -3)
8. (6b3 – 24b -6b2 + 24) ÷ (b2 - 4) = (5b + b -6)
9. (5a2b +4ba -15a - 12) ÷ (ab - 3) = (5a + 4)
10. (p5 + 4p4 - 2p3 - 16p2 -8p) ÷ (p3 – 4p) = (p2 + 4p +2)
11. (x2 + 2x -15) ÷ (x -3) = (x +5) The student should have determined, based on multiplication check that: (x -3)(x +5) = (x2 + 2x -15)
12. (a2 - a -30) ÷ (a - 6) = (a +5) The student should have determined, based on multiplication check that:
(a - 6) (a +5) = (a2 - a -30)
13. (b2 - 6 + 9) ÷ (b -3) = (b -3) The student should have determined, based on multiplication check that: (b -3) (b -3) = (b2 - 6 + 9)
14. (2y2 – 9y + 10) ÷ (y -2) = (2y +5) The student should have determined, based on multiplication check that:
TEACHER MANUAL ALGEBRA II / LESSON 16
(y -2) (2y +5) = (2y2 – 9y + 10)
15. (2m2 – 3m - 9) ÷ (m + 3) = (2m - 3) The student should have determined, based on multiplication check that:
(m + 3) (2m - 3) = (2m2 – 3m - 9)
16. (4a2 + 22a - 12) ÷ (a + 6) = (4a - 2) The student should have determined, based on multiplication check that:
(a + 6)(4a - 2) = (4a2 + 22a - 12)
17. (x3 + 4x3 + x -6) ÷ (x + 2) = (x2 + 2x -3) The student should have determined, based on multiplication check that:
(x + 2)(x2 + 2x -3)= (x3 + 4x3 + x -6)
18. (6b3 – 24b -6b2 + 24) ÷ (b2 - 4) = (5b + b -6) The student should have determined, based on multiplication check that:
(b2 - 4)(5b + b -6) = (6b3 – 24b -6b2 + 24)
19. (5a2b +4ba -15a - 12) ÷ (ab - 3) = (5a + 4) The student should have determined, based on multiplication check that:
(ab - 3)(5a + 4) = (5a2b +4ba -15a - 12)
20. (p5 + 4p4 - 2p3 - 16p2 -8p) ÷ (p3 – 4p) = (p2 + 4p +2) The student should have determined, based on multiplication check that:
(p3 – 4p)(p2 + 4p +2) = (p5 + 4p4 - 2p3 - 16p2 -8p)
Lesson Wrap up: Please review the answers for the problems from the lesson for today with the student. Go over the answers so that they may see which problems they got correct and incorrect. Make sure that the student is clearly writing out all the steps to their process for finding the solution, that way, you can easily go back through their work to see where they may have made simple errors.
TEACHER MANUAL ALGEBRA II / LESSON 18
Answers:
1. 5y10 – 6x7y3 – 4y – 5 = 10
2. x3 +4y - 9 = 3
3. 60x2 y + 8 = 3
4. 4x4 y3 + v y + 7
Leading term: 4x4 y3
Leading coefficient: 4Constant term: 7
5. 8n5 – 4n2 – 2
Leading term: 8n5
Leading coefficient: 8Constant term: -2
6. x8y + x4y + 2 no 7. y2 + 4y + 16 yes/(y + 4) 2 8. (10b8 + 3ab7 + c + 9abc + 4b2) + (1 + c + 4ab7 + 9b2)
= 10b8 + 7ab7 + 2c + 9abc + 13b2 + 1 = 10b8 + 7ab7 + 9abc + 13b2 + 2c + 1
9. (13yx7 + 11yz9 + x + 9 + 8xy2) + (yz9 + 13xy7 + x + 10 + xy2)
= 26xy7+ 12yz9 + 2x + 19 + 9xy2 = 12yz9 + 26xy7+ 9xy2+ 2x + 19
10. (5 + n + 4mo2 + 8n8) + (19 + 16mo2 + 4n10 + 9mno2) + (45 + n)
= 69 + 2n + 20mo2+ 8n8+ 4n10+ 9mno2 = 4n10+ 8n8+ 9mno2+ 20mo2 + 2n + 69
11. (7yx7 + 11y - 8xy2) - (yz9 + 17xy7 - xy2)
= -yz9 -10yx7 - 7xy2 + 11y
12. (34 + n - 4mo2 - 8n8) - (16 + 16mo2 + 12mno2) - (16 + n)
TEACHER MANUAL ALGEBRA II / LESSON 18
= - 8n8 - 12mno2- 20mo2 + 66
13. (- 23xy7 + x + 9 + 8z3) - (5 + 6x) - (7xy7 + 8z3)
= - 30xy7 - 5x + 4
14. (2y - 5) 2 - (y + 6) 2
= 3y 2 - 32y – 9
15. (3m - 4) 2 - (m + 4)2
= 8m 2 - 32m –32
16. (4y + y2) (7xy2 + 6)
= 7x2y3+ 28x2y + 6y2+ 24y
17. (ab + 2b2) (5b2 + 3ab)
= 5b4+ 5a2b2+ 3a2b2 +6ab3
18. (9xyz + 3xy2) (xy2 + 6)
= 9x2y2z + 3x2y2 + 18xyz+ 18xy2
19. (4b + 2b2) (5b2 + 3b)
= 10b4 +26b3 +12b2
20. (7yx7 + 11)(yz9 - 17xy4 + xy2)
= 7y2x7 z9 - 119x8y5 +7x8y3 +11yz9 – 187xy4 -11xy2
21. (4xy2+ 4y + 14) (14yx4 + 4xy2 + 8y)
= 56x5y3 + 48xy6 + 16x2y4 +56y2x4 +196yx4 + 56xy2 + 32y2 + 112y
TEACHER MANUAL ALGEBRA II / LESSON 18
22. ab + 2a2b2 + 3ab = ab 23. 9xyz + 3xy4z+ 3xy2 + 6xz = 3x 24. 4ab + 5ba2 + 3b = b 25. 2yx7 + 10yz9 + xy4 + 5xy2 = xy 26. 4xy2+ 4xy4 + 12xy2 ÷ 4xy2 =y2 + 3y 27. 5m2n2 + 5mno3 + 5mno2 ÷ 5mn = mn+ o3 + o2 28. 14s4t2 - 7s4t2 + 12t2 ÷ t = 14s4t - 7s4t + 12t 29. (2y2 – 9y + 10) ÷ (y -2) = (2y +5)
The student should have also determined, based on the multiplication check that: (y -2)(2y +5) = (2y2 – 9y + 10)
30. (2m2 – 3m - 9) ÷ (m + 3) = (2m - 3)
The student should have also determined, based on the multiplication check that: (m + 3) (2m - 3) = (2m2 – 3m - 9)
Lesson Wrap up: Please review the answers for the problems from the lesson for today with the student. Go over the answers so that they may see which problems they got correct and incorrect. Have the student review and redo any incorrect answers to the problems given in today’s lesson. Let the student know that these will be the concepts covered in the upcoming assessment.