Homework Corrections (Page 1 of 3) A # 14 / Holt 8-4 #36, 39, 42, 45, 48, 51, 54, 67, 68, 70, 77 – 82; Holt 8-3 #33 – 36, 38 – 43 Holt 8-4 36. (3x + 2)(x + 3) 39. (3x – 4)(x – 5) 42. (5x + 3)(2x + 5) 45. (2x – 1)(2x + 3) 48. (n + 1)(3n – 4) 51. -(3x – 2)(x + 1) 54. 5x2 + 31x – 28; (x + 7)(5x – 4) 67. 4x(x + 2) + 1(x + 2) (4x + 1)(x + 2) 68. width increased by 2 yd, length increased by 3 yd 70. The student forgot to find factors of both 12 and 2 77. B
Homework Corrections (Page 2 of 3) A # 14 / Holt 8-4 #36, 39, 42, 45, 48, 51, 54, 67, 68, 70, 77 – 82; Holt 8-3 #33 – 36, 38 – 43 Holt 8-4 cont. 78. H 79. A 80. G 81. (2x + 1)(2x + 1) 82. (7x – 1)(7x – 1) Holt 8-3 33. C 34. A 35. D 36. B 38. (x + 5)(x – 4) 39. (x – 2)(x – 9)
Homework Corrections (Page 3 of 3) A # 14 / Holt 8-4 #36, 39, 42, 45, 48, 51, 54, 67, 68, 70, 77 – 82; Holt 8-3 #33 – 36, 38 – 43 Holt 8-3 cont. 40. (x + 3)(x – 7) 41. (x + 1)(x + 9) 42. (x – 4)(x – 8) 43. (x + 6)(x + 7)
Lesson Objective: I will be able to … Factor perfect square trinomials and difference of two squares Language Objective: I will be able to … Read, write, and listen about vocabulary, key concepts, and examples
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A trinomial is a perfect square if: • The first and last terms are perfect squares. • The middle term is two times one factor from the first term and one factor from the last term. Example: 9x2 + 12x + 4 3x 3x • 2 2 2(3x 2) Page 20
Example 1: Recognizing and Factoring Perfect-Square Trinomials Page 20 Determine whether each trinomial is a perfect square. If so, factor. If not explain. A. 9x2 – 15x + 64 B. 81x2 + 90x + 25 5 5 9x 9x 2(9x 5) ● 8 8 3x 3x 2(3x 8) 2(3x 8) = 48x ≠ 15x 2(9x 5) = 90x 9x2 – 15x + 64 is not a perfect-square trinomial because 15x ≠ 2(3x 8). 81x2 + 90x + 25 is a perfect-square trinomial because 90x = 2(9x 5). 81x2 + 90x + 25 =(9x + 5)2
x2 – 14x + 49 is a perfect-square trinomial because 14x = 2(x 7). Your Turn 1 Page 21 Determine whether each trinomial is a perfect square. If so, factor. If not explain. x2 – 14x + 49 x x 2(x 7) 7 7 2(x 7) = 14x x2 – 14x + 49 is a perfect-square trinomial because 14x = 2(x 7). x2 – 14x + 49 =(x – 7)2
4x2 – 9 2x 2x 3 3 A polynomial is a difference of two squares if: There are two terms, one subtracted from the other. Both terms are perfect squares. Example: 4x2 – 9 2x 2x 3 3 Page 20
Example 2: Recognizing and Factoring the Difference of Two Squares Page 21 Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. A. 100x2 – 4y2 B. x4 – 25y6 2y 2y 10x 10x 5y3 5y3 x2 x2 100x2 – 4y2 is a difference of two squares because and . x4 – 25y6 is a difference of two squares because and . 100x2 – 4y2 = (10x + 2y)(10x – 2y) x4 – 25y6 = (x2 + 5y3)(x2 – 5y3)
Your Turn 2 Page 21 Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 16x2 – 4y5 4x 4x 2y? 2y? 16x2 – 4y5 is not the difference of two squares because 4y5 is not a perfect square.
Classwork Assignment #15 Holt 8-5 #1 – 13
Homework Assignment #15 Holt 8-5 #14 – 19, 21 – 32 KIN 8-6