3-4 Solving Quadatic Equations by Factoring 15. Divide each side of the equation by 2. Write the equation with the right side equals zero.
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1 15. Divide each side of the equation by 2. Write the equation with the right side equals zero. Use the identity (a b) 2 = a 2 2ab + b 2 to factor the left side of the equation. Here, a = x and b = 6. So, (x 6) 2 = 0. Therefore, the root is 6. Write a quadratic equation in standard form with the given root(s). esolutions Manual - Powered by Cognero Page 8
2 19. Write a quadratic equation in standard form with the given root(s). Write the pattern. Replace p and q with Use the FOIL method to multiply. f 6fxt Multiply each side by 5. Factor each polynomial. no necessary esolutions Manual - Powered by Cognero Page 9
3 26. Factor each polynomial. Find the factors of 40 whose sum is 13. 5(8) = 40 and = soo Xt Write 13x as 5x + 8x. Factor x from the first two terms and 8 from the last two terms. Factor x + 5 from the two terms. Therefore, 27. Find the factors of 22 whose sum is 9. 2( 11) = 22 and 2 + ( 11) = 9 Write 9x as 2x 11x. XtDh Factor x from the first two terms and 11 from the last two terms. Factor x + 2 from the two terms. Therefore, esolutions Manual - Powered by Cognero Page 10
4 33. Use the identity a 2 b 2 = (a + b)(a b) notfactor able Therefore, Mao this Solve each equation. 37. Factor out the GCF, 12x. Therefore, the roots are 0 and 9. esolutions Manual - Powered by Cognero Page 11
5 1, Find the factors of 45 whose sum is 4. 9( 5) = 45 and = 4 Write 4x as 5x + 9x. Factor x from the first two terms and 9 from the last two terms. I 45 s 9 S 9 g 3 15 Xt 9 X 51 0 Factor x 5 from the two terms. I 40. Therefore, the roots are 5 and 9. Write the equation with right side equal to zero. Use the identity a 2 b 2 = (a + b)(a b) to factor x THEISM x It Therefore, the roots are 11 and 11. X esolutions Manual - Powered by Cognero Page 12
6 41. Write the equation with right side equal to zero. Use the identity a 2 b 2 = (a + b)(a b) to factor x 2 (-4). IT Therefore, the roots are 2i and 2i. esolutions Manual - Powered by Cognero Page 13
7 42. Factor out 1. Now factor 3x x 8. Here, a = 3, b = 10 and c = 8. ac = 3( 8) = 24 Find two factors of 24 whose sum is ( 2) = 24 and 12 + ( 2) = 10 Write 10x as 12x + ( 2x). Then divide both sides l 1,8 2, x 2 Xt 4 58 Factor 3x from the first two terms and 2 from the last two terms. I Factor x + 4 from the two terms. Therefore, the roots are MOVIE THEATER esolutions Manual - Powered by Cognero Page 14
8 55. MOVIE THEATER A company plans to build a large multiplex theater. The financial analyst told her manager that the profit function for their theater was P(x) = x x 512, where x is the number of movie screens, and P (x) is the profit earned in thousands of dollars. Determine the range of production of movie screens that will guarantee that the company will not lose money. For the company not to loose money, the profit should be non-negative. That is, at least zero. Factor out 1. TF Factor x 2 48x Find factors of 512 whose sum is ( 32) = 512 and 16 + ( 32) = 48 x 48 5,24 Eg X 16 X 34 O 96,6342 L A total of 16 to 32 screens will guarantee that company will not lose money. esolutions Manual - Powered by Cognero Page 15
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Practice Test - Chapter 2
1 State the domain and range of the relation shown in the table Then determine if it is a function If it is a function, determine if it is one-to-one, onto, both, or neither 4 Write 2y = 6x + 4 in standard
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Algebra 1R/H Regents Review 7. x 1, for which value of x is
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Read the following definitions and match them with the appropriate example(s) using the lines provided.
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Practice Test - Chapter 2
Graph and analyze each function. Describe the domain, range, intercepts, end behavior, continuity, and where the function is increasing or decreasing. 1. f (x) = 0.25x 3 Evaluate the function for several
2-4 Solving Equations with the Variable on Each Side. Solve each equation. Check your solution x + 2 = 4x + 38 ANSWER: 4 ANSWER:
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Polynomials: Adding, Subtracting, & Multiplying (5.1 & 5.2)
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Polynomial Operations ACTIVITY 4.2 SUGGESTED LEARNING STRATEGIES: Close Reading, Discussion Group, Create Representations, Think/Pair/Share, Self/Peer Revision and Pizza Supply sells wholesale goods to
Solve each equation by completing the square. Round to the nearest tenth if necessary. 5. x 2 + 4x = 6 ANSWER: 5.2, 1.2
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7-6 Common Logarithms
Use a calculator to evaluate each expression to the nearest ten-thousandth. 1. log 5 KEYSTROKES: LOG 5 ENTER 0.698970043 5. SCIENCE The amount of energy E in ergs that an earthquake releases is related