CP Algebra 2 Unit 2-1: Factoring and Solving Quadratics ...

[Pages:59]CP Algebra 2 Unit 2-1:

Factoring and Solving Quadratics WORKSHEET PACKET

Name:__________________Period______

Learning Targets:

0. I can add, subtract and multiply polynomial expressions

1. I can factor using GCF.

2. I can factor by grouping.

Factoring Quadratic Expressions

3. I can factor when a is one. 4. I can factor when a is not equal to one.

5. I can factor perfect square trinomials.

6. I can factor using difference of squares.

7. I can solve by factoring.

8. I can solve by taking the square root.

Solving Quadratic Equations

9. I can perform operations with imaginary numbers. 10. I can solve by completing the square. 11. I can solve equations using the quadratic formula (with rationalized denominators).

12. I can use the discriminant to determine the number and type of solutions.

13. I can write quadratic equations given the real solutions.

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LT 0 Unit 2-1 CPA2

Name __________________ Pd _______

I can add, subtract and multiply polynomial expressions

Use and attach another sheet of paper for work.

Write the polynomial in standard form. Then state it's degree.

17. 14 + x + 13x2

18. 2 x - 5 x2

33

19. -1 +x2 + 6x3

20. x3 + 5x ? 2x2 + 2 21. -3x2 + 3 - x3

22. -4x3 +6x2 ? 19x + 18

Perform the indicated operation.

23. (6x2 + 1) + (5x2 ? 4)

24. (2x3 + 11x + 2) ? (x3 - 2x + 7)

25. (x2 ? 3x + 3) ? (x2 + x ? 1)

26. (14 ? 16x) + (10x ? 5)

27. (8x3 ? 1) ? (20x3 + 2x2 ? x ? 5)

28. 6x ? (22x + 3 ? 36x2 + x3)

29. (4x2 ? 15x + 16) + (2x - 20) 31. (-3x3 + 4x ? 9) ? (2x3 + x2 ? x)

30. (7x3 ? 2 + x2 + 13x) ? (4x3 + 10) 32.(6x2- 18x + 3) ? (14x2 ? 12x + 9)

33. (15 ? 10x3 ? 2x2 + x) ? (x2 + 7x)

34. (50x ? 3) ? (8x3 + 9x2 + 2x + 4)

35. (4x ? 33 + 9x2) +(20x3 ? 19x + 3) 36. (12x3 ? 5x2 ? 70x +1)+(-17x3 + 56x)

37. x(x2 + 9x ? 5)

38. 12x2(x ? 8)

39. -2x(x + 4)

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LT 0 I can add, subtract and multiply polynomial expressions

Perform the indicated operation.

40. 2x(3x2 - x + 6)

41. (x - 2)(x - 4)

42. (x + 8)(x ? 1)

43. (x+ 3)(x2 ?x - 2)

44. (x+9)(x2 - 6x + 4) 45. (2x ? 1)(3x3 ? x + 3)

46. (6x + 2)(2x2 + x + 1) 47. (x+9)(x2 ? 2x + 6) 48. (2x- 3)(4x2 ? 3x + 3)

Write the polynomial in standard form. Show work!

49. (x+9)(x-9) 50. (x+2)(x-2) 51.(x + 5)2

52. (x ? 3)2

53. (x ? 4)3

54. (x + 6)3

55. (x+1)3

56. (3x+ 4)2

17 ? 56 even 18) - 5 x2 + 2 x , 2 33

20) x3 - 2x2 + 5x + 2 , 3

22) -4x3 + 6x2 - 19x + 18 , 3

24) x3 + 13x - 5

26) ?6x + 9

28) ?x3 + 36x2 ? 16x ? 3 30) 3x3 + x2 + 13x ?12

32) ?8x2 ? 6x ? 634) ?8x3 ? 9x2 + 48x ? 7

36) ?5x3 ? 5x2 ? 14x + 1

38) 12x3 ? 96x2 40) 6x3 ? 2x2 + 12x

42) x2 + 7x ? 8 44) x3 + 3x2 ? 50x + 36

46) 12x3 + 10x2 + 8x + 2 48) 8x3 ? 18x2 + 15x ? 9

50) x2 ? 4

52) x2 ? 6x + 9

54) x3 + 18x2 + 108x + 216 56) 9x2 + 24x + 16

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.LT 1 I can factor using GCF.

Name_____________________________

Factoring by pulling out the Greatest Common Factor

Factor completely. Write PRIME is the polynomial does not factor:

1) 5ax ? 5a

2) 5xz + 2xy ? 3yz

3) 24ab4 + 12ab3 - 18ab2

4) 3n2 + 9

5) x(x +y) ? y(x+y)

6) 25k3 + 20k2 + 10k

7) 8x2 + 5x ? 7

8) 7ab5 ? 56ab

9) mnx2 ? nx2 + m3x

10) x2(x2 ? 5) + 6(x2 ? 5)

11) 6k3 ? 18k2

12) 12m7 ? 8m5 + 20m3

13) 6xy ? 6xz ? 6x

14) 3x4 + 12x2 ? 33

15) 8a4b4 ? 28a3b3 + 4a2b2

16) 4k2 + 18k3 - 6k4

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LT 2 I can factor by grouping. Factoring by Grouping

17) x2 + 3x + xk + 3k

18) a2 - 2a + ad - 2d

19) uv + 5u + v2 + 5v 21) 2ab + 14a + b + 7

20) m3 + m2n + mn2 + n3

22) 5x2y + x2 ? 10y ? 2

23) 2br + 8b ? 3r ? 12

24) x2 + 3x ? xy ? 3y

25) ac ? ad + bc ? bd

26) 3x2 + 6x ? y + 3

27) x4 + x3 ? 7x ? 7

28) y3 + 3y2 + 3y + 9

29) y3 + y2 + 2y + 2

30) 10a + 10b + xa + xb

Answers Scrambled

prime 2k2(2 + 9k - 3k2) 7ab(b4 - 8) 6k2(k - 3) (x + y)(x - y) prime 3(x4 + 4x2 - 11) 3(n2 + 3) 6x(y - z - 1) x(mnx - nx + m3) 5a(x - 1) 4m3(3m4 - 2m2 + 5)

Look for the answer you have & lightly cross it out.

6ab2 ( 4b2 + 2b - 3) 4a2b2 (2a2b2 - 7ab + 1) 5k( 5k2 + 4k + 2)

(x+3)(x-y)

(a+b)(c-d)

prime (2b-3)(r+4) (x+3)(x+k) (10+x)(a+b)

(a+d)(a-2) (m2+n2)(m+n) (5y+1)(x2-2) (y+3)(y2+3)

(2a+1)(b+7)

(v+5)(u+v) (y+1)(y2+2) (x2 - 5)(x2 + 6)

(x+1)(x3-7)

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LT 6 I can factor using difference of squares. Name___________________________

Factoring the Difference of Squares

1) x2 ? 25 = (

)(

)

2) x2 ? 144 = (

)(

)

3) 9x2 ? y2 =

4) 9 ? x2

5) 2x2 ? 32

6) 2x3 ? 18x

7) x2 ? 1

8) 15a3b3 ? 18a5b2 + 24ab4

9) 16x2 ? 9

10) x2 + 4

11) 64x2 ? 81

12) 625 ? x4

13) 4x2 ? 9

14) 2x(3x + 1) ? (3x + 1)

15) 5x2 ? 125

16) 49x2y2?25z2

17) 30x2y ? 24xy2 + 36x3y

18) 25x4 ? 4

19) x4 ? 81

20) x2 + 2x + 7x + 14

21) x2y2z2 ? 36

22) x2 ? y2

23) 9x2 ? 1

24) (2z ? 3)2 ? (x + 7y)2

25) (x + y)2 ? z2

26) 6x + xy + 6y + y2

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LT 6 I can factor using difference of squares.

27) (x ? y)2 ? (y ? 8)2

28) (a + b)2 ? (c + 5)2

29) x3 + x2y ? xy2 ? y3

30) (x ? 5)2 ? y2

31) x2 ? (y + 2)2

32) 16x2 + 49y2

33) (x ? 6)2 ? 9y2

34) (3x + y)2 ? (2x + 5)2

35) 169 ? 49x2

36) 100 ? (x + 9y)2

37) ?x2 + 25

38) 2x3 ? 6x2 + 3x ? 9

39) ? x2 + 100

40) x2 + 1

ANSWERS SCRAMBLED

(3x+1)(2x?1) (x2+9)(x+3)(x?3)

(2z?3+x+7y)(2z?3?x?7y)

prime 6xy(5x?4y+6x2)

2x(x+3)(x?3) 3ab2(5a2b?6a4+8b2)

(x+y)(x?y)

(x?5+y)(x?5?y)

(8x+9)(8x?9)

(x+y+2)(x?y?2)

(x+12)(x?12) (25+x2)(5+x)(5?x)

(3+x)(3?x)

(x?6+3y)(x?6?3y) (5+x)(5?x) (6+y)(x+y) (4x+3)(4x?3) (x?8)(x?2y+8) (2x+3)(2x?3) (10+x+9y)(10?x?9y) (x+2)(x+7) (3x+y)(3x?y) 2(x+4)(x?4) (13?7x)(13+7x) prime (x?3)(2x2+3) (x+3)(x-y)

(x+5)(x?5) 5(x+5)(x?5) (x+y+z)(x+y?z) (x+1)(x?1) prime (10+x)(10?x) (5x2+2)(5x2?2) (xyz+6)(xyz?6) (3x+1)(3x?1) (x+y)(x+y)(x?y) (7xy+5z)(7xy?5z) (5x+y+5)(x+y?5) (a+b+c+5)(a+b?c?5)

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Factoring TRINOMIALS Name__________________________

LT 3 and 4 . I can factor when a is one and I can factor when a is not equal to one.

1) X2 - X - 42

2) X2 + 4X - 21

3) X2 - 2X - 63

4) X2 - 11X + 18

5) 2X2 + 9X - 18

6) 3X2 + 10X - 8

7) X2 - 18X + 72 9) X2 - 9X + 18 11) 3X2 + 5X + 2 13) 4X2 - 17X - 15 15) 8X2 - 6X - 5 17) 6X2 + 19X + 3

8) X2 - 7X + 6 10) 6X2 - X - 15 12) 2X2 - X - 15 14) 8X2 - 25X + 3 16) 8X2 + 10X - 3 18) 6X2 + X - 2

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