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Lesson 5 Ex5

4-26 Honors Algebra Warm-up. A square with side length x is cut from a right triangle shown at the right. What value of x will result in a figure that is 3/4 of the area of the original triangle? Show how you arrived at your answer .

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Lesson 5 Ex5

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  1. 4-26 Honors Algebra Warm-up A square with side length x is cut from a right triangle shown at the right. What value of x will result in a figure that is 3/4 of the area of the original triangle? Show how you arrived at your answer. There are multiple ways to get the answer, check with a partner to make sure your way is reasonable. Answer: x = 4 units Lesson 5 Ex5

  2. HW: p.451 #11-31odd, 32, 34 • Check odds in the back of the book. • Sample: 8(2n +3) cm by (n – 1) cm • 34. 3in x 12in x 2in Key Concept 806a

  3. FOIL (3x + 4)(3x – 4)= (3x + 4)2 = (3x – 4)2 = = 9x2 – 16 Difference of Two Squares = 9x2 + 24x + 16 Perfect Square Trinomial = 9x2 – 24x + 16 Perfect Square Trinonmial

  4. Method 6: Factoring Perfect Square Trinomials • 1. Check the trinomial to see if it is of the form • a2 + 2ab + b2 or a2- 2ab + b2 • 3 conditions • The first term must be a perfect square (a2) • The last term must be a perfect square (b)2 • The middle term must be twice the product of the square roots of the first and last terms 2(a)(b). • If a2 + 2ab + b2, write as (a + b)2 • If a2 - 2ab + b2, write as (a - b)2

  5. Factor Perfect Square Trinomials A. Determine whether 25x2 – 30x + 9 is a perfect square trinomial. If so, factor it. 1. Is the first term a perfect square? Yes, 25x2 = (5x)2. 2. Is the last term a perfect square? Yes, 9 = 32. 3. Is the middle term equal to 2(5x)(3)? Yes, 30x = 2(5x)(3). Answer:Yes, (5x – 3)2 Factor using the pattern. Lesson 6 Ex1

  6. Factor Perfect Square Trinomials B. Determine whether 49y2 + 42y + 36 is a perfect square trinomial. If so, factor it. 1. Is the first term a perfect square? Yes, 49y2 = (7y)2. 2. Is the last term a perfect square? Yes, 36 = 62. 3. Is the middle term equal to 2(7y)(6)? No, 42y≠ 2(7y)(6). Answer: 49y2 + 42y + 36 is not a perfect square trinomial. Lesson 6 Ex1

  7. Factor Completely Factor 16y2 + 8y – 15. First check for GCF, then check for perfect square trinomial. Since 16y2+ 8y – 15 is not a perfect square trinomial, use ax2 + bx + c. = 16y2 + 20y – 12y – 15 m= 20 and n= –12 = (16y2 + 20y) + (–12y – 15) Group = 4y(4y + 5) – 3(4y + 5) Factor out the GCF Answer: (4y + 5)(4y – 3) Lesson 6 Ex2

  8. Solve Equations with Repeated Factors Solve 4x2 + 36x + 81 = 0. (2x + 9)2 = 0 Factor the perfect square trinomial. 2x + 9 = 0 Set the repeated factor equal to zero. 2x = –9 Solve for x. Lesson 6 Ex3

  9. Key Concept 8-6c

  10. Use the Square Root Property to Solve Equations A. Solve (b – 7)2 = 36. b – 7 = ±6 Square Root Property b = 7± 6 Add 7 to each side. b = 7 + 6 or b = 7 – 6 Separate into two equations. = 13 = 1 Simplify. Answer:{1, 13} Lesson 6 Ex5

  11. B. Solve the equation (x – 4)2 = 25. Check your solution. • A • B • C • D A. {–1, 9} B. {–1} C. {9} D. {0, 9} Lesson 6 CYP5

  12. Concept Summary 8-6b

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