CP Algebra 2 Unit 2-1: Factoring and Solving Quadratics WORKSHEET PACKET

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CP Algebra Unit -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.

1 CP Algebra Unit -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.. 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. 9. I can perform operations with imaginary numbers. Solving Quadratic Equations 10. I can solve by completing the square. 11. I can solve equations using the quadratic formula (with rationalized denominators). 1. I can use the discriminant to determine the number and type of solutions. 13. I can write quadratic equations given the real solutions. 1

2 LT 0 Unit -1 CPA 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 x + 13x x 5 3 x x + 6x 3 0. x 3 + 5x x x x 3. -4x 3 +6x 19x + 18 Perform the indicated operation. 3. (6x + 1) + (5x 4) 4. (x x + ) (x 3 - x + 7) 5. (x 3x + 3) (x + x 1) 6. (14 16x) + (10x 5) 7. (8x 3 1) (0x 3 + x x 5) 8. 6x (x x + x 3 ) 9. (4x 15x + 16) + (x - 0) 30. (7x 3 + x + 13x) (4x ) 31. (-3x 3 + 4x 9) (x 3 + x x) 3.(6x - 18x + 3) (14x 1x + 9) 33. (15 10x 3 x + x) (x + 7x) 34. (50x 3) (8x 3 + 9x + x + 4) 35. (4x x ) +(0x 3 19x + 3) 36. (1x 3 5x 70x +1)+(-17x x) 37. x(x + 9x 5) 38. 1x (x 8) 39. -x(x + 4)

3 LT 0 I can add, subtract and multiply polynomial expressions Perform the indicated operation. 40. x(3x - x + 6) 41. (x - )(x - 4) 4. (x + 8)(x 1) 43. (x+ 3)(x x - ) 44. (x+9)(x - 6x + 4) 45. (x 1)(3x 3 x + 3) 46. (6x + )(x + x + 1) 47. (x+9)(x x + 6) 48. (x- 3)(4x 3x + 3) Write the polynomial in standard form. Show work! 49. (x+9)(x-9) 50. (x+)(x-) 51.(x + 5) 5. (x 3) 53. (x 4) (x + 6) (x+1) (3x+ 4) even 18) x + x, 0) x x + 5x +, ) 4x + 6x 19x + 18, 3 4) x + 13x 5 6) 6x + 9 8) x x 16x 3 30) 3x 3 + x + 13x 1 3) 8x 6x 634) 8x 3 9x + 48x 7 36) 5x 3 5x 14x ) 1x 3 96x 40) 6x 3 x + 1x 4) x + 7x 8 44) x 3 + 3x 50x ) 1x x + 8x + 48) 8x 3 18x + 15x 9 50) x 4 5) x 6x ) x x + 108x ) 9x + 4x

4 .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 ) 5xz + xy 3yz 4 3 3) 4ab + 1ab 18ab 4) 3n + 9 5) x(x +y) y(x+y) 6) 5k 3 + 0k + 10k 7) 8x + 5x 7 8) 7ab 5 56ab 9) mnx nx + m 3 x 10) x (x 5) + 6(x 5) 11) 6k 3 18k 1) 1m 7 8m 5 + 0m 3 13) 6xy 6xz 6x 14) 3x 4 + 1x ) 8a 4 b 4 8a 3 b 3 + 4a b 16) 4k + 18k 6k 4

5 LT I can factor by grouping. Factoring by Grouping 17) x + 3x + xk + 3k 18) a a + ad d 19) uv + 5u + v + 5v 0) m 3 + m n + mn + n 3 1) ab + 14a + b + 7 ) 5x y + x 10y 3) br + 8b 3r 1 4) x + 3x xy 3y 5) ac ad + bc bd 6) 3x + 6x y + 3 7) x 4 + x 3 7x 7 8) y 3 + 3y + 3y + 9 9) y 3 + y + y + 30) 10a + 10b + xa + xb Answers Scrambled Look for the answer you have & lightly cross it out. prime 6ab ( 4b + b - 3) k ( + 9k - 3k ) 4a b (a b - 7ab + 1) 7ab(b 4-8) 5k( 5k + 4k + ) 6k (k - 3) (x + y)(x - y) (x+3)(x-y) (a+b)(c-d) prime prime (a+d)(a-) 3(x 4 + 4x - 11) (b-3)(r+4) (m +n )(m+n) 3(n + 3) (x+3)(x+k) (5y+1)(x -) 6x(y - z - 1) (10+x)(a+b) (y+3)(y +3) x(mnx - nx + m 3 ) (a+1)(b+7) 5a(x - 1) (v+5)(u+v) 4m 3 (3m 4 - m + 5) (y+1)(y +) (x - 5)(x + 6) (x+1)(x 3-7) 5

6 LT 6 I can factor using difference of squares. Name Factoring the Difference of Squares 1) x 5 = ( )( ) ) x 144 = ( )( ) 3) 9x y = 4) 9 x 5) x 3 6) x 3 18x 7) x 1 8) 15a 3 b 3 18a 5 b + 4ab 4 9) 16x 9 10) x ) 64x 81 1) 65 x 4 13) 4x 9 14) x(3x + 1) (3x + 1) 15) 5x 15 16) 49x y 5z 17) 30x y 4xy + 36x 3 y 18) 5x ) x ) x + x + 7x ) x y z 36 ) x y 3) 9x 1 4) (z 3) (x + 7y) 5) (x + y) z 6) 6x + xy + 6y + y 6

7 LT 6 I can factor using difference of squares. 7) (x y) (y 8) 8) (a + b) (c + 5) 9) x 3 + x y xy y 3 30) (x 5) y 31) x (y + ) 3) 16x + 49y 33) (x 6) 9y 34) (3x + y) (x + 5) 35) x 36) 100 (x + 9y) 37) x ) x 3 6x + 3x 9 39) x ) x + 1 ANSWERS SCRAMBLED (3x+1)(x 1) (x 6+3y)(x 6 3y) (x+5)(x 5) (x +9)(x+3)(x 3) (5+x)(5 x) 5(x+5)(x 5) (z 3+x+7y)(z 3 x 7y) (6+y)(x+y) (x+y+z)(x+y z) prime (4x+3)(4x 3) (x+1)(x 1) 6xy(5x 4y+6x ) (x 8)(x y+8) prime x(x+3)(x 3) (x+3)(x 3) (10+x)(10 x) 3ab (5a b 6a 4 +8b ) (10+x+9y)(10 x 9y) (5x +)(5x ) (x+y)(x y) (x+)(x+7) (xyz+6)(xyz 6) (x 5+y)(x 5 y) (3x+y)(3x y) (3x+1)(3x 1) (8x+9)(8x 9) (x+4)(x 4) (x+y)(x+y)(x y) (x+y+)(x y ) (13 7x)(13+7x) (7xy+5z)(7xy 5z) (x+1)(x 1) prime (5x+y+5)(x+y 5) (5+x )(5+x)(5 x) (x 3)(x +3) (a+b+c+5)(a+b c 5) (3+x)(3 x) (x+3)(x-y) 7

8 Name LT 3 and 4. I can factor when a is one and I can factor when a is not equal to one. Factoring TRINOMIALS 1) X X 4 ) X + 4X 1 3) X X 63 4) X 11X ) X + 9X 18 6) 3X + 10X 8 7) X 18X + 7 8) X 7X + 6 9) X 9X ) 6X X 15 11) 3X + 5X + 1) X X 15 13) 4X 17X 15 14) 8X 5X ) 8X 6X 5 16) 8X + 10X 3 17) 6X + 19X ) 6X + X 8

9 LT 3 and 4. I can factor when a is one and I can factor when a is not equal to one. 19) 6X 17X 3 0) 8X X 15 1) 3X 15X + 18 ) 7X + X ) X + 11X + 10X 4) 8X 18X 3 3 5) 5X 40X + 60X 6) 4X + 8X ) X + 8X 0X 8) 10X Y 5X Y 35XY 3 9) 3X Y 10X Y + 8XY 30) 15X Y 10XY 5Y MIXED-UP ANSWERS (x - 6) (x - 1) (6x + 1) (x + 3) (x - 3) (x + 6) 5x (x - 6) (x - ) 4(x + 5) (x - 3) x (x + 10) (x - ) (6x +1) (x - 3) prime (4x + 3) (x - 5) (x - 7) (x + 6) xy (3x - 4) (x - ) 5y (3x - 5) (x + 1) 3(x - 3) (x - ) (4x - 1) (x + 3) (3x - 5) (x + 3) (3x + ) (x + 1) x (x + 10) (x + 1) (3x + ) (x - 1) 5xy (x - 7) (x + 1) (x - 9) (x - ) x (x + 3) (x - 3) (3x - ) (x + 4) (4x + 5) (x - 3) (x - 6) (x - 3) (x + 5) (x - 3) (8x - 1) (x - 3) (x - 9) (x + 7) (x + 1) (4x - 5) (x - 6) (x - 1) (x + 7) (x - 3) 9

10 LT 1-6 Mixed Factoring Name Pd Use and attach another sheet of paper for work. Factor completely with respect to the integers x x x x 3 x + 4x x x + 3x x 3 + x + 5x x 3 x + 4x x x +7x x 3 4x 3x x 3 + 4x + 4x x x +3x x 3 - x + 5x x 3 + 3x -3x x 3-0x +3x x 3 - x + 7x

11 LT 1-6 Mixed Factoring 39. 7x x + 7x 40. 3x - 4x x 3-4x -3x x 3-18x x x 4-300x 46. 8x 3 7x 47. 3x 4 + 3x 3 + 6x + 6x 48. x 4 + 1x 3 + 4x + 48x x 3-0x - x x 3-9x 18x even 16) 3(x+4)(x 4) 8) (10x +1)(3x+4) 30) (x +4)(x ) 3) ( x 3)(x+) or 1(x +3)(x+) 34) (6x +1)(3x+5) 36) (x+4)(x 4)(x+3) 38) (x +3)(9x 1) 40) 3(x 4) 4) (3x 1)(x-3) 46) 7x(x+1)(x 1) 48) x(x +4)(x+1) 50) 9(x+1)(x 1)(x 1) 11

12 CP Algebra Name LT 1-6 Review of Factoring Simplify Completely: 4 3 1) ( x 3x x + 1) + ( x x + x 6) + ) ( 3 x 6)( x + 5) 3) ( 4 x + 3) 3 4) ( x 3) Factor Completely. Write PRIME if it can't be factored: 5) 3a b + 6ab 6) x 16 8) x 1 9) 5x + x 4 x 3 11) a + 3a + 5a ) 16x ) x + 1x + 16x 14) 4x + 8x 3x 6 3 LT 1-6 Review of Factoring 1

13 15) xw + xy + xz 16) x x 30 4 y 3 z x + 18) 5x 3 45x 17) ( ) 0) 6x + 8x 3x 4 1) x ) y y + 16y 8 3) x + x 3 3 5) ( a + b) ( a 3 b ) 4) 4x 1x 40x 4m 3 n m 5n + 6) ( ) ( ) ANSWERS: 1) 4 3 x + x + x x 5 ) 6x + 3x 30 3) 3 64x + 144x + 108x + 7 4) 4x 1x + 9 5) 3 ab( a + ) 6) ( x 4)( x + 4) 8) ( x 4)( x + 3) 9) ( 5 x 4)( x + 1) 11) (a + 5)(a + 3) 1) (4x + 7)(4x - 7) 13) x(x + 1x + 16) 14) (4x 3)(x + ) 15) x(w + y + z) 16) (x +5)(x - 6) 17) (x+y+3z)(x y 3z) 18) 5x(x + 3)(x - 3) 0) (x - 1)(3x +4) 1) (x 4 + 1)(x + 1)(x - 1)(x + 1) ) (y + )(y y + 4)(y - 1) 3) (x+1)((x-1)(x + 3) 4) 4x(x 5)(x + ) 5) (3a b)(-a + 5b) 6) 4(3m - n)(-m - 4n) or 4(3m - n)(m + 4n) 13

14 CP Algebra - Name LT 1-6 Review of Factoring Simplify Completely: 3 3 1) ( 6x 4x + 5) ( x + 6x 7) ) 3 6x ( 4x 3x + 5) 3) ( x 3)( (4x 6x + 1) x + 4) ( ) 3 Factor Completely. Write PRIME if it can't be factored: 3 5) 4x y x y 6) 5 x 8) x 7x ) 8x + 6x ) x x y 4x + 4y 1) 5x ) x 13x 36x 14) 9y 6y + 1y ) ax ay az 16) ( ) x + y z 14

15 LT 1-6 Review of Factoring 17) 3x 3 48x 19) 3xy 9x + y 3 0) x ) x + 3x 7x ) x x 8 3) 3x + 9x 1x 3 5x 4 y 3x + y 4) ( ) ( ) ANSWERS 3 1) 4x 10x + 1 ) 4x x 4 30x 3 3) 8x 3 16x + 3 4) x 3 6x + 1x 8 5) x y(x - 1) 6) (5 + x)(5 - x) 8) (x - 5)(x - ) 9) (4x +3 )(x + 5) 11) (x 3 4)(x y) 1) prime 13) x(x 13x 36) 14) (3y + 4) (3y - ) 15) a(x y z) 16) (x + y + z)(x + y z) 17) 3x(x + 4)(x 4) 19) (y 3)(3x + 1) 0) (x + 9)(x + 3)(x - 3) 1) (x+3)(x-3)(x +3x+ 9) ) (x-)(x+)(x +) 3) 3x(x + 4)(x - 1) 4) 4(4x y)(-x+3y) or -4(4x y)(x-3y) 15

16 Unit 1 LT 3 I can simplify square roots Name Simplify each square root 1) 8 = ) 45 = 3) 50 4) 1 5) 98 6) 48 7) 15 8) 0 9) 7 10) 63 11) 144 1) 3 13) 75 14) 00 ANSWERS SCRAMBLED

17 Unit 1 LT 3 I can simplify square roots 15) 5 18 = 5 16) 3 8 = 17) ) 1000,, ) ) 8 7 1) 4 80 ) ) ) ) 500 6) 4 4 7) ) ANSWERS SCRAMBLED

18 LT 1 6 Name Class Date Practice 5-4Factoring Quadratic Expressions - Factor each expression completely. 1. x + 4x + 4. x 7x x + 7x 8 4. x 6x 5. x 9x x + x x + 6x x 9 9. x 13x x x + x 1. x 9x x x x x x 16. x x x x x x 1. 4x x x 4 5. x 7x 8 6. x + 13x x 5x x + 5x x 1x 30. x + 13x x 5x 3 3. x + 10x x 14x x + 4x x 5x x + 13x x 7x x + 16x x + 5x x + 34x x 11x 4. 3x + 1x 43. x + 8x x 10x x + 7x x x x x x x x + 17x x 17x x + 1x x 4x x x + 6x x x + 18x x x + 1x x + 0x x + 30x x 6x x 3x x x x x 10x x + 8x x x x + x x 11x x + 4x x 5x x + x x 3x

19 LT7. I can solve by factoring. LT 8. I can solve by taking the square root. Name Practice 5-5 Quadratic Equations Solve each equation by factoring, by taking square roots, or by graphing. When necessary, round your answer to the nearest hundredth. 1. x 18x 40 = 0. 16x = 56x 3. 5x = 15x 4. x 6x 7 = 0 5. x 49 = 0 6. x + x + 1 = 0 7. x 1 = 0 8. x 3x 4 = 0 9. x + 9x + 0 = x + 9 = 55x 11. (x + 5) = x 3x = x + x 10 = x + 3x = x 6x + 1 = x + 1 = 4x 17. x + = 3x 18. 6x + 1 = 5x 19. x x + 1 = x + 5x = 1. x 6x = 8. x + 6 = 7x 3. 6x + 18x = 0 4. x + 5 = 11x 5. 3x 7x + = 0 6. x 3x = 1 7. x x = 6 8. x 144 = x + = 6x 30. 5x + = 7x 31. 7x + 6x 1 = 0 3. x 6x = x 1x + 1 = x + 1 = 8x 35. x + 9 = 10x 36. (x ) = x 8x + 7 = x 16 = x + 6x = x + 3 = 4x 41. x + 6 = 7x 4. 6x + = 7x 43. (x + 7) = x 8x = x + 7x + 1 = x + = 9x 47. 3x + 4 = 8x 48. 4x x = x + 10x = x + 9x + 4 = x + 6x = x 1 = 10x 53. 4x = x = 1x 55. 5x 9 = x + 11x = x 6x + 1 = x + 11 = 1x 59. 6x + = 13x 60. x = x 11x = x + 6x + 1 = x + 9x + 8 = x + 8x = x + 6x = x = x = x x + x 6 = x 1 = x + 4x = x 105 = x = x + 5x + 4 = x + 36 = 13x 75. x + 6 = 5x 19

20 LT 8. I can solve by taking the square root. LT 9. I can perform operations with imaginary numbers. Practice 5-6 Complex Numbers Name LT 9. I can perform operations with imaginary numbers Simplify each expression (1 + 5i) + (1 5i) 30. (3 + i) (3 + i) ( + 6i) (7 + 9i) 33. (1 + 5i)(1 5i) 34. (1 + 5i)(6 3i) 35. (5 6i)(6 i) 36. (3 + 4i)(3 + 4i) 37. ( + 3i)( 3i) 38. ( + i)( i) 39. ( 3 i)(1 3i) 40. (3 + 3i) (4 3i) (4 i)(4 i) 46. (4 + i)(1 7i) 47. (1 + 3i)(1 7i) 48. ( + 4i)( 3 i) 49. (11 1i)(11 + 1i) 50. ( + 3i) + ( 4 + 5i) 51. (5 + 14i) (10 i) 5. (5 + 1i)(5 1i) 53. (3 + 4i)(1 i) 54. (6 + i)(1 i) 55. (5 13i)(5 13i) ( + 3i)(4 + 5i) 60. (5 + 4i) ( 1 i) 61. (1 + i)( 1 i) 6. ( 1 + 4i)(1 i) 63. (6 + i) + (1 i) 64. (3 + i)(3 + i) 65. ( + 3i) + (4 + 5i) 66. (5 + 4i)(1 + i) 67. ( 1 5i)( 1 + 5i) LT 8. I can solve by taking the square root. Solve each equation. 68. x + 80 = x = x + 40 = x + 36 = x + 75 = x = x = x + 1 = x + 10 = x = x + 9 = x + 90 = 0 0

21 LT10. I can solve by completing the square. Name Practice 5-7 Completing the Square Complete the square. 1. x + 6x +!. x 7x +! 3. x + 1x +! 4. x + 3x +! 5. x 8x +! 6. x + 16x +! 7. x + 1x +! 8. x x +! Solve each quadratic equation by completing the square. 4. x + 1x + 4 = 0 5. x x 5 = x = 1x 3 7. x x 1 = x 8x + 1 = x = 8x x 4x 3 = x + 11x = 0 3. x = 5x x + x 1 = x + 6x 7 = x = 8x x = 3x x = x x = 6x x = 7x x = 3x x = 6x 9 4. x = 3x x = 7x x = 3x x = 4x x = 5x x = 6x x = 3x 49. x = 8x 50. 4x = x x = x x = 5x x = 5x x = x x = 7x x = 6x x = 7x x = 5x 59. 3x = 4x 60. x = 4x x = x x = 3x x = 3x x = x x = x + 4 Solve each equation. 66. x + x + 1 = x 18x + 7 = x 4x + 4 = x + 3x+ 9 4 = x + 3x+ 9 4 = x + 3x =

22 LT 1. I can use the discriminant to determine the number and type of solutions. LT 11. I can solve equations using the quadratic formula (with rationalized denominators). Name Class Date Practice 5-8 The Quadratic Formula LT 1. I can use the discriminant to determine the number and type of solutions. Evaluate the discriminant of each equation. Tell how many solutions each equation has and whether the solutions are real or imaginary. 1 y = x + 10x 5. y = x + 10x y = 9x 4x 4. y = 4x 4x y = 4x 5x y = 4x 3x y = x + 3x y = x + 7x 3 9. y = x + 3x y = x 5x y = x + 1x y = x + x y = x 13x y = 5x + 6x y = 4x 4x 1 LT 11. I can solve equations using the quadratic formula (with rationalized denominators). Solve each equation using the Quadratic Formula. 16. x + 6x + 9 = x 15x + 56 = x 5x + = x + 3x + 5 = x 3x + 1 = x + x 5 = 0. x + 8x + 15 = x + x + 1 = x + x + 5 = 0 5. x 4x 1 = 0 6. x = 3x + 7. x 5x + = 0 8. x + 6x 4 = 0 9. x = x x + 7 = 6x 31. x + 6x + 3 = 0 3. x = 18x x + 9x 13 = x 8x + 5 = x + 13x = x 5x = x + 4x + 5 = x = 3x x + x + 1 = x + x + 3 = x + x = x x + 7 = x x + 3 = x + 3x = x = 5x x + 6x + 5 = x 6x = x 6x = 6 Solve: 49. A model of the daily profits p of a gas station based on the price per gallon g is p = - 15,000g + 34,500g 16,800. Use the discriminant to find whether the station can profit $4000 per day. Explain. Solve each equation using the Quadratic Formula. Find the exact solutions. Then approximate any radical solutions. Round to the nearest hundredth. 50. x x 3 = x + 5x + 4 = 0 5. x x 8 = x 1x + 3 = x + 5x 1 = x + 5x + 1 = x + 5x 4 = x + x = x 13x = x + 5x = x + 3x 3 = x 4x + 1 = x 6x 7 = x 35 = x 64. x + 7x + 10 = 0

23 LT 1. I can use the discriminant to determine the number and type of solutions. CP Algebra 5.8 Name Discriminant Fill in the chart: Equation Standard Form Discriminant Number and type of Roots 1. 6x + 3x + 4 = 0. x = -6x x 6 = -5x 4. x x = -4 3

24 Review LT 7-13 Name 1. Solve the following equations by the square root method. Solve for all solutions, including imaginary numbers. a. 8x 70 =11x +5 b. 9x 13 = 0. Solve the following quadratic equations by factoring. a. 4x +16x +1 = 0 b. 3x 10x +8 = 0 c. x 64 = 0 5. Rewrite each number in the standard form for complex numbers, a + bi. Reduce fractions and simplify radicals. a. 11 b. ( 3 10i) + ( 6 5i) c. 7 6 d. i 3 e. i 4 f. ( 1 i) ( 4 + 3i) g. ( 5+ i) 3i ( ) 4

25 Review LT Use the Quadratic Formula to solve x + x +1= 0 7. Use completing the square to solve the following equation. x +10x 3 = 0 8. Solve the following equations for real solutions only. a. 5x = 15 b. 3y +11= Find the discriminant of the following quadratic equations and put it on the first blank. On the second blank, state the number of real solutions for the equation. a. 3x 4x + 5 = x + 3 real solutions b. x +8x +8 = 0 real solutions 13. Solve the following equations for real or imaginary solutions using the method indicated. Carefully show all of the work and simplify your answers as much as possible to simplified radical form and/or the standard form for complex numbers. a. x + 0x +80 = 0 completing the square a. 5

26 b. x + 3x = 5 completing the square b. c. x 9x = 3x + 10x Quadratic Formula c. d. 5x + x + 3 = 0 Quadratic Formula d. 15. Find the approximate real roots (or real zeros) of the following quadratic equation, rounded to the nearest hundredth. y = 3x + x 6 a) no real roots b) -1.75, 1.15 c) 1.08, d) 1.1,

27 CP Algebra Name LT 7. I can solve by factoring. LT 10. I can solve by completing the square. Factor if possible. Use completing the square for those that don t factor. 1) X + 10X 4 = 0 ) X + 1X = 8 = 0 Ans. X = or X = 3) X + 18X + 56 = 0 4) X 6X = 5 5) X 9X + 0 = 0 6) X 5X = 50 7) X = 8X 15 8) X X = 1 7

28 LT 7. I can solve by factoring. LT 10. I can solve by completing the square. Steps to solve a quadratic equation by Completing the Square: 1) Make sure the coefficient of X is 1. (If it isn t, divide by the number!) ) Put the constant on the right side. 3) Take 1 of the coefficient of X, square it, and add it to both sides. 4) Factor & Solve Solve by completing the square: 9) 4X + 8X 1 = 0 10) X 4X 8 = 0 11) X 6X 10 = 0 1) X + X 6 = 0 ANSWERS: 1), 1 ), 14 3) 4, 14 4) 3 ± 14 5) 5, 4 6) 5, 10 7) 5, 3 8) 1 ± 5 9) 1, 3 10) 1± 5 11) 3 ± 9 1) 3, 8

29 LT 7,8,10,11 Solving Equations Solve for x: Name 1) x + 7x+ 10= 0 ) x 8x+ 1= 0 3) x 49= 0 x =, 4) x + 5x 6 = 0 5) x 7x 18= 0 6) x 5x = 0 7) x + 5x 3 = 0 8) 3x 8x + 4 = 0 9) x 3x 5 = 0 9

30 LT 7,8,10,11 Solving Equations 10) 3x + x 10 = 0 11) 4x 5 = 0 1) x + 7x = 0 13) 5x + 9x + 0 = 0 14) 6x 19x + 15 = 0 Answers Scrambled (+ that don t match anything!) 3, 1 5 { },6 3 5, ,, 1, 3 7 { }, 5 0, { } 6,1 4, 5 { } 5 0,5 { } 7, 7 3 5, 1,, 3 3 { },9 30

31 NAME I. Solve using the square root method. LT 7,8,10,11 Solving Equations (1) () Don t Forget ± Symbol! x = x = II. Solve by completing the square. (3) (4) 1) ) half of b, square it,& add it to both sides. 3) change trinomial, to (binomial) 4) square root method x = x = III. Solve using the quadratic formula. ***Get in standard form first! (5) (6) x = x = V. Use the discriminant to determine the number of real solutions. (+), (0) 1, ( ) 0 (8) VII. Simplify. 10) (18-5i)+(-3+11i) i0 = 1, i = 1, i = 1, i3 = i 11) (+5i)-(3-i) 1) (3+7i)(4-8i) 31

32 Unit 1 LT 3 Did you Hear About.. Rationalizing Radicals in denominators 3

33 LT 8 and 10 D-51 Square Root method or Completing the Square Cooking 33

34 LT 10 D-5 Completing the Square Title of the Picture 34

35 LT 1 D-55 Discriminant and Number of Solutions Soil Erosion 35

36 CP Algebra Name DO YOU REMEMBER Unit 1? 1) Write an equation of the line through the points (,-3) and (-1,0). ) Solve: x 5 = 3 3) Solve: 7x 3( x ) = ( 5 x ) 4) Solve the system : x y = 16 x y = 5) Solve the system: y = x + 7 4x y = - 3 6) Find the x and y intercepts of the line 3y x = 4 7) Evaluate: 3x + 4x when x = 8) Solve for x: (3 - (x + 4)) - 5(x - 7) = 3x - x 4 ANSWERS 1) y = x 1 5) (,11) ) x = 4, 1 6)(0, 4/3) (-4,0) 3) x = 3 7) 0 4) (4, -6) 8) x = 9 36

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Multiplication of Polynomials

Multiplication of Polynomials Summary 391 Chapter 5 SUMMARY Section 5.1 A polynomial in x is defined by a finite sum of terms of the form ax n, where a is a real number and n is a whole number. a is the coefficient of the term. n is