Additional Exercises 7.1 Form I The Greatest Common Factor and Factoring by Grouping Find the greatest common factor of each list of monomials. 1. 10x and 15 x 1.. 3 1y and 8y. 3. 16 a 3 a, 4 and 4 3a 3. 3 4. 6 x y, 15x y and 4 1x 4. Factor the greatest common factor from the polynomial. If there is no factor other then 1 and the polynomial cannot be factored, so state. 5. 5x + 0 5. 6. 6 a 3 a + 18 6. 3 7. 3y + 5y + 6y 7. 4 8. 4x + 18x 1x 8. 4 3 3 9. 16x y 0x y + 1xy 9. 10. 5 4 4 3 3 4x y + 10x y 14x y 10. AE-7
Factor out the common binomial factor from each polynomial. 11. x ( y + 14) + 6( y + 14) 11. 1. a ( b 7) 3( b 7) 1. 13. 11 ( x + 10) y( x + 10) 13. Factor by grouping. 14. xy + 4 y + x + 8 14. 15. ab + 3b 6a 18 15. 16. xy 5y + x 5 16. 17. x 3 x + x 4 17. 18. 6 ab + b + 9a + 3 18. 19. 5xy + y 10x 4 19. 4 3 0. x x + x 0. AE-8
Additional Exercises 7.1 Form II The Greatest Common Factor and Factoring by Grouping Find the greatest common factor of each list of monomials. 1. 1x and 0 x 1.. 45 y x and xy 36. 3. 64 b 9 a and 88 b 5 9 a 3. 4. 4 n 5 3 4 4 m n, 18m and 30 n 3 m 4. Factor the greatest common factor from the polynomial. If there is no factor other then 1 and the polynomial cannot be factored, so state. 5. 14 x 3 x + 1 5. 6. 6 x 5 7 x 5 6. 7. 9 5 3 30a 15 7. 4a + a 8. 6 3 5 4 3 6 0x y 44x y + 36x y 8. 9. 8 8 3 6 6 4 40x y 16x y 0x y 9. 10. 6 5 4 3 3 4 4 15x y 5x y + 55x y 60x y 10. AE-9
Factor out the common binomial factor from each polynomial. 11. x ( y 7) ( y 7) 11. 1. a ( b + 3) + 4( b + 3) 1. 13. 4a (8 + b) (8 + b) 13. Factor by grouping. 14. x 3 x 3x + 6 14. 15. xy + 5 y + 4x + 0 15. 3 16. b + ab + 4b + 8a 16. 17. 6 xy + 4y + 15x + 10 17. 18. 14 xy x 1y + 3 18. 4 3 19. 4x 8x 3x + 6 19. 0. 3 3 + 15a b 16ab 1 0. 0a b AE-30
Additional Exercises 7.1 Form III The Greatest Common Factor and Factoring by Grouping Find the greatest common factor of each list of monomials. 1. 4 8x and 4x 1.. 18 x 8 6 x, 45 and 4 1x. 3. 1 y 6 4 9 x y, 30x and 84 y 5 5 x 3. Factor the greatest common factor from the polynomial. If there is no factor other then 1 and the polynomial cannot be factored, so state. 3 4. 1y 9y + 1y 4. 5. 3x xy 5 3 3 + 4x y 96 5. 3 6. 0a 15a + 5a 6. 7. 8 9 6 6 4 3 48x y + 40x y + 64x y 7. 8. 3 3 16m n 48n n 64mn 8. Factor out the common binomial factor from each polynomial. 9. x ( x 3) + 6( x 3) 9. 10. y ( x + 7) ( x + 7) 10. AE-31
11. 6x (x 7) + (x 7) 11. Factor by grouping. 4 3 1. x 3x 4x + 1x 1. 13. ab 4b + 6a 4b 13. 14. 10xy + 16y 5x 8 14. 15. 6mn + n 7m 9 15. 3 16. 9x 6x + 15x 10 16. 4 3 17. 0x 5x + 1x 15x 17. 18. 3 1a 16a 9a + 1 18. Solve. 19. The area of a rectangle is x + 6xy + 4xy + 1y. The width 19. of the rectangle is x + 3y. Write a polynomial for the length of the rectangle. 0. The width of a rectangle is x + y. The length of the rectangle 0. is x 5. Write a polynomial for the area of the rectangle. AE-3
Additional Exercises 7. Form I Factoring Trinomials Whose Leading Coefficient is 1 Factor each trinomial, or state that the trinomial is prime. 1. x + 5x + 4 1.. x + 7x + 1. 3. y + 8y + 1 3. 4. a 6a + 8 4. 5. x 8x + 15 5. 6. y 8y + 7 6. 7. a + a 6 7. 8. x 3x 40 8. 9. m 3m 4 9. 10. a + 4ab 1b 10. AE-33
11. a 6xy 7 y 11. 1. x 6xy 7y 1. 13. a 11a + 30 13. 14. x + 11x + 8 14. Factor each trinomial completely. 15. x 4x 6 15. 16. 3a 15a + 18 16. 17. x 3 + 7x + 6x 17. 18. x 3 y + x y 35xy 18. 19. 4x 3x + 48 19. 3 0. 8a + 56a + 96a 0. AE-34
Additional Exercises 7. Form II Factoring Trinomials Whose Leading Coefficient is 1 Factor each trinomial, or state that the trinomial is prime. 1. x + 10x + 16 1.. x 10x + 4. 3. x x 30 3. 4. a + 10a + 1 4. 5. y + 9y 36 5. 6. x 15x + 54 6. 7. x + 5x 36 7. 8. a + 14a + 33 8. 9. m + 6m + 10 9. 10. x 11x + 10 10. AE-35
11. y + y 4 11. 1. a + 9a + 0 1. 13. x 9x 8 13. 14. y 1y + 3 14. Factor each trinomial completely. 15. 5x + 10x 15 15. 16. 4x + 8x + 48 16. 17. x 4 3 + x 48x 17. 3 18. a + 18a + 40a 18. 19. x 3 y + 3x y 40xy 19. 3 0. 6y + 66y + 148y 0. AE-36
Additional Exercises 7. Form III Factoring Trinomials Whose Leading Coefficient is 1 Factor each trinomial, or state that the trinomial is prime. 1. x + 14x + 45 1.. a 5a 4. 3. y + 9y + 14 3. 4. x 18x + 3 4. 5. x 13x + 1 5. 6. y 3y 88 6. 7. a + 15ab 16b 7. 8. x + 3x + 1 8. 9. y 16y + 39 9. 10. a 5a + 136 10. AE-37
11. x + + 1xy 54y 11. 1. y 8y + 1 1. 13. a 11a + 8 13. 14. x 11xy 60y 14. Factor each trinomial completely. 3 15. 4x 8x + 16x 15. 16. 5x 30x 80 16. 3 17. 3a + 7a + 60a 17. 4 3 18. x y + x y 4x y 18. 3 19. 6y 30y 16 19. 0. 8x + xy 3 + 56x y 96 0. AE-38
Additional Exercises 7.3 Form I Factoring Trinomials Whose Leading Coefficient is Not 1 Use the method of your choice to factor each trinomial, or state that the trinomial is prime. 1. x + 9x + 4 1.. 3x + 16x + 5. 3. 4a + 11a + 6 3. 4. 3x + x 16 4. 5. y y 15 5. 6. 3x 14x 5 6. 7. 4a 13a + 10 7. 8. 6x 19x + 3 8. 9. 6y 13y + 6 9. 10. 8x + 6x + 1 10. AE-39
11. 10x 17x + 3 11. 1. 1y + 4y 5 1. 13. 16a 34a 15 13. Factor completely. 14. 6x + 6x + 8 14. 15. 4x 66x + 15 15. 16. 10a a 4 3 + a 16. 3 17. 8y + 8y + 4y 17. 18. 3x x 4 3 4x 4 18. 3 19. 8a 18a 18a 19. 0. 10x + 45x + 50 0. AE-40
Additional Exercises 7.3 Form II Factoring Trinomials Whose Leading Coefficient is Not 1 Use the method of your choice to factor each trinomial, or state that the trinomial is prime. 1. 6x + 11x + 3 1.. 4x + 11x + 6. 3. 10x + 7x + 5 3. 4. 8x 14x + 5 4. 5. 1x 5x + 5 5. 6. 10x + x 4 6. 7. 8x + 33x + 4 7. 8. 14x + 17x 6 8. 9. 6x 7x 10 9. 10. 16x 8x 15 10. AE-41
11. 1x y + 5xy 9 11. 1. 16x + 34x 15 1. 13. 3x y 5xy 8 13. Factor completely. 14. 8a + 1a + 4 14. 15. 18a + 66a 4 15. 16. 0y 35y 10 16. 3 17. 1x + 18x + 4x 17. 3 18. 1a 1a 45a 18. 3 19. 3y + 68y 30y 19. 0. 48x 40x 3 0. AE-4
Additional Exercises 7.3 Form III Factoring Trinomials Whose Leading Coefficient is Not 1 Use the method of your choice to factor each polynomial, or state that the polynomial is prime. 1. 7x + 18x + 11 1.. a a 8. 3. x + 7x + 1 3. 4. 15x + 8x + 1 4. 5. 9x + 14x 8 5. 6. 10a + 7a 1 6. 7. 4y + 9y 4 7. 8. 15x y + xy 8. 9. x + 4 3 + 7x 6x 9. 10. 15b + 14b 8 10. AE-43
11. 0x + 1x 7 11. 1. 4x y 14xy 8 1. 13. 10a 11a + 18 13. 14. 4x + 35x 4 14. 15. 1a + 19a + 4 15. 16. 18y 78y 60 16. 17. 60x + y + 35xy 5 17. 18. 8x 30x + 5 18. 19. 3 4 5 6 16x y + 40x y + 5xy 19. 0. The area of a rectangle is 36x + 66x + 30. If the length is 0. 6 x + 6, express the width as a binomial. AE-44
Factor each difference of two squares. Additional Exercises 7.4 Form I Factoring Special Forms 1. x 64 1.. a 1. 3. y 100 3. 4. 4x 5 4. Factor any perfect square trinomials, or state that the polynomial is prime. 5. x + 10x + 5 5. 6. y + 6y + 9 6. 7. a 8a + 16 7. 8. a 0a + 100 8. Factor each sum or difference of two cubes. 9. x 3 1 9. AE-45
10. y 3 + 64 10. 11. 3 3 x 8y 11. 1. 3 3 a + 7b 1. Factor each polynomial completely, or state that the polynomial is prime. 13. x 13. 14. 3x 4x + 48 14. 15. x 3 16x 15. 16. 5y + 0y + 0 16. 17. 7x 8 17. 18. 100 y x 400 18. 19. 4a 40a + 100 19. 0. 8x + 48x + 7 0. AE-46
Factor each difference of two squares. Additional Exercises 7.4 Form II Factoring Special Forms 1. x 11 1.. 4a 81. 3. 16y 169 3. 4. x 5 4. Factor any perfect square trinomials, or state that the polynomial is prime. 5. x 4x + 4 5. 6. y + 3y + 9 6. 7. x + 10xy 5y 7. 8. 4x + 6xy + 9 8. Factor each sum or difference of two cubes. 9. x 3 1000 9. AE-47
10. 3 3 a + 8b 10. 11. y 3 7 11. 1. 5x + y + 30xy 9 1. Factor each polynomial completely, or state that the polynomial is prime. 13. 5x 0 13. 14. 1x + 60x + 75 14. 15. x + 5 15. 16. 4 3 ab 64a b 16. 17. 9y 3 9y 17. 3 18. 1x + 84x + 147x 18. 19. x 4 16 19. 0. 0x 15 0. AE-48
Factor each difference of two squares. Additional Exercises 7.4 Form III Factoring Special Forms 1. 49x 64 1.. y + 16. 3. x 1x + 36 3. 4. 18a 7 4. 5. 9x 30x + 5 5. 6. 3x + 48x + 18 6. 7. 3 3 a + 15b 7. 8. 49x + 14x + 1 8. 9. 4x + y 3 36xy 81 9. 10. 3 8 m 10. AE-49
11. 3x 98 11. 1. 16 y x + 64 1. 13. 0x + y + 100xy 15 13. 14. 54 y 4 3 x + 18 14. 15. 5x + 11 15. 16. 16 b 3 3 a 54 16. 17. 81m + n + 34mn 169 17. 18. 6 4 x 81y 18. 19. ( x + 8) 4 19. 0. 5a + 150a + 5 0. AE-50
Additional Exercises 7.5 Form I A General Factoring Strategy Factor each polynomial completely, or state that the polynomial is prime. 1. x 64 1.. 8x + 10x 3. 3. a 14a + 14 3. 4. 3x 18 4. 5. 10x + 17x + 3 5. 6. x + 9x + 14 6. 7. x 4 3 + 4x 1x 7. 8. xy + 5y 4x 0 8. 9. a + 4a + 9. 10. y 3 5y 4y 10. AE-51
11. 6m + 17m + 1 11. 1. 4x 64 1. 13. x 3 8x + 4x 3 13. 14. 14x 7x 105 14. 15. y 3 16 15. 16. 16 b a + 9 16. 17. 4 x 5 3 x 8 17. 3 18. 30x y 9x y 1xy 18. 19. 40x 3 5 19. 0. 4x y + 16y 3x 18 0. AE-5
Additional Exercises 7.5 Form II A General Factoring Strategy Factor each polynomial completely, or state that the polynomial is prime. 1. y 3 64 1.. 3x 75. 3. 16x 16x 60 3. 4. x y 4x + 6y 4 4, 5. 1x 5x + 3 5. 6. 36 y x 5 6. 7. 4a 3 + 56 7. 8. 5 xy 3 x y 4 8. 9. 6x + 84x + 94 9. 10. 1x + 41x + 4 10. AE-53
11. 48y 3 6 11. 1. 18xy 1x + 45y 10 1. 13. 16a + 81 13. 14. 3 3 4 a b + a b + ab 14. 15. 48x 64x 35 15. 16. 4x + 8x + 5 16. 17. 3 b 3 3 a 375 17. 18. 16x 4 81 18. 3 19. 18x + 1x + x 19. 3 3 3 3 0. x y 3xy + 4x 1x 0. AE-54
Additional Exercises 7.5 Form III A General Factoring Strategy Factor each polynomial completely, or state that the polynomial is prime. 1. a 4 81 1.. 18x + 9x 35. 3. 8y 3 15 3. 4. 1x y + 9x 8y 6 4. 5. 44a + 44a 33 5. 6. 64y 5 6. 7. 5x y + 14x y 4xy 7. 8. 40a b + 3a 50ab 40ab 8. 9. 36y 84y + 49 9. 10. 81x 4 65 10. AE-55
11. 45a 10a + 80 11. 1. 16x + y + 0xy 5 1. 13. 3 3 4 18x y 5x y 50xy 13. 14. 54a 3 + 16 14. 15. 5y 100 15. 16. 10x 1x 108 16. 17. 6 6 x y 17. 18. 45x + 16x 7 18. 19. 6 6 a 8b 19. 0. 16 b 10 10 a + 9 0. AE-56
Date Additional Exercises 7.6 Form I Solving Quadratic Equations by Factoring Solve each equation using the zero product principle. 1. ( x 9)( x + 7) = 0 1.. ( y + 1)( y + 8) = 0. 3. ( 3x + 1)(x 1) = 0 3. 4. x ( x 5) = 0 4. 5. x ( x + 3)(5x 4) = 0 5. Use factoring to solve each quadratic equation. 6. x 5x + 4 = 0 6. 7. 3x 10x 8 = 0 7. 8. x x = 0 8. 9. x + 4x = 1 9. AE-57
Date 10. 6x = x 10. 11. y = 49 11. 1. 3x 7x + 60 = 0 1. 13. 8x 8x = 10 13. 14. x ( x 5) = 1 14. 15. 18y 30y = 0 15. 16. 9x = 1x 4 16. Solve. 17. The width of a rectangle is 6 meters less than the length. 17. The area of the rectangle is 40 square meters. Find the dimensions of the rectangle. 18. An object is thrown upward from the top of a 160 foot 18. building with an initial velocity of 48 feet per second. The height h of the object after t seconds is given by the quadratic equation h = 16t + 48t + 160. How long will it take for the object to hit the ground? AE-58
Date Additional Exercises 7.6 Form II Solving Quadratic Equations by Factoring Solve each equation using the zero product principle. 1. ( x 7)( x 10) = 0 1.. ( y + 4)( y + 1) = 0. 3. ( 5x 4)( x + 9) = 0 3. 4. x ( x + 6)( x 7) = 0 4. 5. 4 x ( x + 3)(4x 7) = 0 5. Use factoring to solve each quadratic equation. 6. y 9y + 8 = 0 6. 7. 4x + 13x 1 = 0 7. 8. 5x 3x = 10 8. 9. 4x 5 = 0 9. AE-59
Date 10. 3x 0x = 7 10. 11. x (4x + 13) = 7 11. 1. 3x = 14x + 80 1. 13. 5y + 5y + 6 = 0 13. 14. 4x + 4x = 0 14. 15. x = 3 + 15x 8x 15. 16. 4x ( x = x + ) 9 16. Solve. 17. The length of a rectangle is 8 inches less than twice the width. 17. If the area of the rectangle is 90 square inches, what are the dimensions of the rectangle? 18. A window washer accidentally drops a bucket from the top of a 18. 64 foot building. The height h of the bucket after t seconds is given by the quadratic equation h = 16t + 64. When will the bucket hit the ground? AE-60
Date Additional Exercises 7.6 Form III Solving Quadratic Equations by Factoring Solve each equation using the zero product principle. 1. ( 7x + 4)( x ) = 0 1.. ( x 8)(3x 10) = 0. 3. x ( 3x + 15) = 0 3. 4. y ( y + 17) = 0 4. 5. x ( 5x 1)( x 8) = 0 5. Use factoring to solve each quadratic equation. 6. 5x 4x 9 = 0 6. 7. x 4x = 5 7. 8. 13y 6y = 0 8. 9. 16x = 5 9. AE-61
Date 10. 4x = 0x 5 10. 3 11. 16x + 8x = 30x 11. 1. x ( 3x 5) = 8 1. 13. x ( 5x + 8) = 4 13. 14. 3x 3 75x = 0 14. 15. y( y + 5) = (36 y) 15. 16. 5 x ( x 5) = 3( x + 4) 16. Solve. 17. The length of a rectangle is 6 feet less than twice the width. 17. If the area of the rectangle is 16 square feet, find the dimensions of the rectangle. 18. If the sides of a square are increased by meters, the area 18. becomes 64 square meters. Find the length of a side of the original square. 19. A window washer accidentally drops a bucket from the top of 19. a 100 foot tall building. The height h of the bucket after t seconds is given by h = 16t +100. How long will it be before the bucket hits the ground? 0. Each cycle of a screen saver program generates and then erases 0. numbers of little animated figures called froobies. The formula P = x + 106x 674 models the population, P, of froobies after x minutes within a cycle. How many minutes into a cycle will the froobie population first reach 118? AE-6