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Secondary Math 2H Unit 3 Factoring and Solving Quadratics Review

1. In your own words, explain what it means to completely factor a polynomial. 2. In your own words, explain how to determine whether a polynomial is prime. 3. In your own words, explain how to recognize a difference of squares. Factor completely. Don’t forget to factor out a GCF if there is one. If the leading coefficient is negative, factor out a negative GCF. If the polynomial is prime, say so.4. 210 5x x− 5. 2 6 14x x+ + 6. 2 4z − 7. 2 4 21v v− − 8. 4 8 2rt r t− + − 9. 2 3 10w w+ − 10. 3 215 5 6 2m m m+ − − 11. 27 15 4t t+ − 12. 312 21w− +

13. 218 200x − 14. 25 25 60p p− + 15. 2 9x + 16. 24 20 24k k− − + 17. 24 5 6n n− − 18. 4 3 26 10 36 60n n n n+ + + 19. 22 13 20q q− + 20. 275 12u − 21. 210 35 20y y− + + 22. 5 412 36 8p q p q pq+ + 23. 3 23 15 42r r r+ − 24. 249 16m − 25. 264 t− 26. 29 24 16a a+ + 27. 2 6 9m m− +

Find the zeros of each function in factored form of a quadratic equation. 28. ( )4 0x x+ = 29. 14 x − 2( ) 4x +5( ) = 0

Find the zeros of each function in standard form by factoring. 30. 2 2 35 0x x− − = 31. 2 9 0x − = 32. 220 10x x= 33. 26 7 90x x= + Write an equation for each problem and then find the solution. Round decimal answers to the nearest hundredth. You must show your work!!! 34. Find two consecutive odd integers whose product is 143. 35. The product of two numbers is 168. One number is ten more than twice the other number. Find the two numbers.

Find all solutions (real and imaginary) to each equation by taking square roots. Write all answers in simplest radical form and write complex answers in the form .a bi+ 36. 2 24b = 37. 26 3 15k − = − 38. ( )23 1 6 33w− − = − 39. ( )22 3 20p+ =

40. 21254x− =

41.

219 43

z⎛ ⎞− + =⎜ ⎟⎝ ⎠

42. A rock is thrown upward off the top of a cliff. It’s height in feet after t seconds is given by the formula

2( ) 16 280h t t= − + . a. What is the height of the cliff? (In other words, how high is the rock at )

b. How high is the rock after 1.5 seconds?

c. How long does it take for the rock to hit the ground? (hint: when the rock hits the ground the height will be 0 so h(t)=0)

0?t =

Solve each equation by completing the square. 43. 2 16 84 0x x+ + = 44. 2 18 92x x= − 45. 2 20 10x x+ =

46. 2 3 12 2

x x− = 47. 29 18 54 0x x− − = 48. 28 16 10x x= − +

Find the discriminant of each quadratic equation and state the number and type of solutions. 49. 22 8 8 0k k− + = 50. 22 5 2 0r r− − − = 51. 23 5 7t t− − = − Solve each equation using the quadratic formula. 52. 2 5 24 0x x− − = 53. 24 8 1x x− = − 54. 27 2 2h h+ = 55. 22 1 0x + =