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Algebra I Chapter 8

Algebra I Chapter 8

CommonMisconceptionYou

CommonMisconceptionYou may be temptedto try to solve theequation in Example 4bby dividing each side ofthe equation by x.Remember, however,that x is an unknownquantity. If you divideby x, you may actuallybe dividing by zero,which is undefined.b. x 2 = 7xWrite the equation so that it is of the form ab = 0.x 2 = 7xOriginal equationx 2 - 7x = 0Subtract 7x from each side.x(x - 7) = 0 Factor using the GCF of x 2 and -7x, which is x.x = 0 or x - 7 = 0 Zero Product Propertyx = 7 Solve each equation.The roots are 0 and 7. Check by substituting 0 and 7 for x in the original equation.4A. 3n(n + 2) = 0 4B. 7 d 2 - 35d = 0 4C. x 2 = -10xPersonal Tutor at ca.algebra1.comExamples 1–3(pp. 426–427)Example 4(pp. 428–429)Factor each polynomial.1. 9 x 2 + 36x 2. 4 r 2 + 8rs + 28r3. 5 y 2 - 15y + 4y - 12 4. 5c - 10 c 2 + 2d - 4cdSolve each equation. Check the solutions.5. h(h + 5) = 06. (n - 4)(n + 2) = 07. 5m = 3 m 28. PHYSICAL SCIENCE A flare is launched froma life raft. The height h of the flare in feetabove the sea is modeled by the formulah = 100t - 16 t 2 , where t is the time inseconds after the flare is launched. Leth = 0 and solve 0 = 100t - 16 t 2 for t. Howmany seconds will it take for the flare toreturn to the sea? Explain your reasoning.100 ft/sh 100t 16t 2h 0HELPHOMEWORKFor SeeExercises Examples9–14 115–20 2, 321–30 4Factor each polynomial.9. 5x + 30y 10. a 5 b - a11. 14gh - 18h212. 8b c + 24bc13. 15 x 2 y 2 + 25xy + x3 214. 12a x + 20b x + 32cx15. x 2 + 2x + 3x + 6 16. 12 y 2 + 9y + 8y + 617. 18 x 2 - 30x - 3x + 5 18. 2my + 7x + 7m + 2xy19. 8ax - 6x - 12a + 9 20. 10 x 2 - 14xy - 15x + 21yLesson 8-2 Factoring Using the Distributive Property 429

Solve each equation. Check the solutions.21. x(x - 24) = 0 22. a(a + 16) = 023. (q + 4)(3q - 15) = 0 24. (3y + 9)(y - 7) = 025. (2b - 3)(3b - 8) = 0 26. (4n + 5)(3n - 7) = 027. 3 z 2 + 12z = 0 28. 2 x 2 = 5x29. BASEBALL Malik popped a ball straight up with an initial upward velocityof 45 feet per second. The height h, in feet, of the ball above the ground ismodeled by the equation h = 2 + 48t - 16 t 2 . How long was the ball in theair if the catcher catches the ball when it is 2 feet above the ground? Isyour answer reasonable in the context of this situation?30. MARINE BIOLOGY In a pool at an aquarium, a dolphin jumps out of thewater traveling at 20 feet per second. Its height h, in feet, above the waterafter t seconds is given by the formula h = 20t - 16 t 2 . Solve the equationfor h = 0 and interpret the solution.Real-World CareerMarine BiologistA marine biologist usesmath to study andanalyze factors thataffect organisms living inand near the ocean.For more information,go to ca.algebra1.com.Factor each polynomial.31. 12 x 2 y 2 z + 40x y3z 2 32. 18 a 2 b c2- 48ab c3GEOMETRY Find an expression for the area of a square with thegiven perimeter.33. P = (12x + 20y) in. 34. P = (36a - 16b) cm35. GEOMETRY The expression _ 1 2 n 2 - _ 3 n can be used to find the number of2diagonals in a polygon that has n sides. Write the expression in factoredform and find the number of diagonals in a decagon (10-sided polygon).SOFTBALL For Exercises 36 and 37, use the following information.Alisha is scheduling the games for a softball league. To find the number ofgames she needs to schedule, she uses the equation g = _ 1 2 n 2 - _ 1 n, where g2represents the number of games needed for each team to play each otherexactly once and n represents the number of teams.36. Write this equation in factored form.37. How many games are needed for 7 teams to play each other exactly3 times?GEOMETRY Write an expression in factored form for the area of eachshaded region.PRACTICEEXTRASee pages 733, 751.38.39. Self-Check Quiz atca.algebra1.comH.O.T. Problems40. REASONING Represent 4 x 2 + 12x as a product of factors in three differentways. Then decide which of the three is the completely factored form.Explain your reasoning.430 Chapter 8 Factoring

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