1. 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. There are multiple ways to get the answer, check with a partner to make sure your way is reasonable. Answer: x = 4 units

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

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

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

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

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

7. Lesson 6 Ex2 Factor Completely First check for GCF, then check for perfect square trinomial. Since 16y 2 + 8y – 15 is not a perfect square trinomial, = 16y 2 + 20y – 12y – 15 m = 20 and n = –12 = (16y 2 + 20y) + (–12y – 15) Group = 4y(4y + 5) – 3(4y + 5) Factor out the GCF Answer: (4y + 5)(4y – 3) use ax 2 + bx + c. Factor 16y 2 + 8y – 15.

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

9. Key Concept 8-6c

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

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

12. Concept Summary 8-6b