algebra ii cover - the ogburn...

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


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.


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


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


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.


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Answers:

1. (10b2 + 3abc + c) - (abc + 4b2)


= 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


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.


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)


= -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


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.


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.


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:


(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.


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)


= - 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


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.

algebra ii cover - the ogburn...

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