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TEST 3 REVIEW MATH 082 Chapter 6 -Factoring polynomials Always look for a common factor first Difference of squares Perfect square trinomials Trinomial w/leading coefficient of 1 Trinomial w/leading coefficient not 1 Factor by grouping 1. 2π₯ 2 β 4π₯ + 20 8. 12π₯ 2 + 7π₯ β 10 2. π₯ 2 β 121 9. 10π₯ 2 β 56π₯ β 24 3. 5π¦ 2 β 20 10. 9β2 β 30β + 25 4. 16π2 β 49π 2 11. π₯ 3 β 4π₯ 2 + 3π₯ β 12 5. π₯ 2 β 21π₯ + 110 12. π¦ 4 + 7π¦ 3 β 9π¦ β 63 6. 3π¦ 2 β 3π¦ β 168 13. π₯ 3 + 2π₯ 2 β π₯ β 2 7. π₯ 2 + 16π₯ + 64 -Solve quadratic equations by factoring Put equation in general form, ax2 + bx + c = 0 (set equal to zero) Then factor. Set factors = 0 Solve (and check answers) 14. (2π¦ β 1)(6π¦ + 7) = 0 15. 4π¦ 2 + 22π¦ β 12 = 0 16. π₯(π₯ β 5) = 84 -Applications with quadratic equations Consecutive integers (odd and even) Free-falling objects Geometry (perimeter and area of squares, triangles, and rectangles) Write an equation and solve each of the following: 17. Find two positive consecutive integers, whose product is 182. 18. Find two positive consecutive odd integers, whose product is 143. 19. An object is dropped from a platform 64 feet above the ground. Itβs height above the ground after t seconds, is given by the equation, β = β16π‘ 2 + 64. When will it hit the ground? 20. The height of a triangle is one inch more than the base. If the area of the triangle is 45 square inches, what is the length of the base and height? 21. The length of a rectangular table is twice as long as itβs width. If the area of the table is 288 square inches, what are the dimensions of the table? Chapter 7 - Find the restricted values of a rational expression. (These are the numbers that make the denominator equal to 0) Find the restricted values of the following rational expressions 22. β2 π₯ 2 β3π₯ 23. π₯+8 π₯ 2 β25 -Simplify a rational expression Remember to factor everything first. Remember that b β a = ο (a β b) Simplify the following expressions. 24. 25. 26. 8π2 π3 β20ππ6 3π₯ 2 β5π₯β2 6π₯ 2 βπ₯β1 π¦ 2 +4π¦β21 27β6π¦βπ¦ 2 -Multiply and divide rational expressions. Remember: Only factors can be cancelled. 27. 28. β2π3 5π4 π¦β2 π¦ 2 +2π¦ β β 15π 12π2 π¦ 2 +8π¦ π¦ 2 +6π¦β16 29. 30. π₯+3 π₯β4 ÷ π₯ 2 βπ₯β12 π₯ 2 β2π₯β8 π¦2 β36 (π¦ β 6) ÷ π¦+1 -Add and subtract rational expressions. 1.Find a common denominator 2. rewrite expressions 3. perform operation 4. simplify 31. 32. 33. 2π₯ 2π₯ 2 βπ₯β3 7 π¦β3 β 3π₯ 4π₯+1 + 5 2π₯β3 5 3βπ¦ β 9 3π₯β1 -Simplify a complex fraction Change to a division problem then invert the divisor and multiply (Remember: Only factors can be cancelled.) 34. 4π3 10π2 16π4 35π3 35. π₯+3 π₯β5 2π₯+6 π₯2 β25 -Solve Rational Equations. multiply both sides by the LCD 36. 37. β3 4π₯ + 2 π₯β7 5 π₯2 = = 2 4π₯ 2 30 π₯ 2 +π₯β56 β 3 π₯+8 38. π₯ 2 = π₯+40 π₯ -Applications of Rational Equations Proportions Similar Triangles Work Rate Motion 39. If a high school employs 9 teachers for every 77 students, how many students are in the school if it employs 234 teachers? 40. Find the unknown length n for the given similar triangles. 12 cm n cm 20 cm 15 41. Jameson can mow the lawn in 40 minutes, while Tyler takes 30 minutes. If they mow the lawn together how long will it take? 42. A plane can fly 500 miles against the wind in the same amount of time that it can fly 725 miles with the wind. If the wind speed is 45 mph, find the speed of the plane in still air.