The solutions are the coordinates of the points on the
line with equation 5x + 4y = 20.- 6 x 2 - 11 x - 10 63. 24m2 - 34m + 7
- 5x 2 + 53x + 72 65. decrease of 25% 66. increase
of 25% 67. increase of 25% 68. decrease of 12.5% - 6x(2x 3 + 5x 2 + 7) 70. 9(8x 3 + 6 x 2 + 3)
- 7x(5x 2 + x + 9)
Lesson 8-5 pp. 51 2-5 17
Go t It? 1.(r+8)(r+3) 2a. (y - 4)(y - 2)
b. No. There are no factors of 2 with sum - 1.
3a. (n + 12)(n - 3) b. (c - 7)(c + 3) 4. x + 8
and x - 9 5. (m + 9n)(m - 3ri)
Lesso n Ch eck 1. (x + 4)(x + 3) 2. (r - 7 )(r- 6 )- (p + 8 )(p - 5) 4. (a + 4b)(a + 8 b) 5. n - 7 and
n + 4 6. positive 7. positive 8. negative 9. when the
constant term is positive and the coefficient of the
second term is negative
Ex e r c i se s 1 1. 2 1 3. 2 1 5. (f + 2)(f + 8 ) - (n - 7 ){n - 8 ) 19. (q - 6 )(q - 2) 21. 6 23. 1
- (w+ 1)(w - 8 ) 2 7. (x+ 6 )(x -1)
- (n + 2)(n - 5) 31. r-4 and r+ 1 33. A
- (r+9s)(/-+10s) 37. (m - 7n)(m + An)
- (w— 1 0 z )(w - 4z) 41a. p and q must have the
same sign. b. p and q must have opposite signs. - x- 12 45. 4x 2 + 12x + 5; (2 x + 5 ) (2 x + 1 )
47a. They are opposites, b. Since the coefficient of the
middle term is negative, the number with the greater
absolute value must be negative. So, p must be a negative
integer. 49. (x + 25)(x + 2) 51. (k - 21)(k + 3) - (s + 5t)(s - 15f) 55. (x 6 + 7)(x 6 + 5)
- (r3 - 16)(r3 - 5) 59. (x 6 - 24)(x6 + 5) 61. C
- A 65. c 2 + 8 c + 16 66. 4v2 - 36v + 81
- 9w2 - 49 68. y 69. §r 70. mn-c 71. 7x
- 6 73. 3
Lesson 8-6 pp. 5 18-5 22Go t It? 1a. (3x + 5)(2x + 1) b. The factors are both
negative. 2. (2x + 7)(5x - 2) 3. 2x + 3 and 4x + 5
- 4(2x + 1 )(x - 5)
Lesso n Ch eck 1. (3x + 1 )(x + 5) 2. (5g + 2)(2g + 1)
3. (2w - 1 )(2w + 3) 4. 3x + 8 and 2x - 9 5. There are
no factors of 20 with sum 7. 6. 24 7. Answers may vary.
Sample: If a = 1, you look for factors of c whose sum is
b. If a + 1, you look for factors of ac whose sum is b.
Ex e r c i se s 9. (3d + 2)(d + 7 ) 11. (4p + 3)(p + 1)
13. (2g-3)(4g- 1) 15. {2k + 3){k - 8 )
17. (3x — 4)(x + 9) 19. (2c/+5)(2d-7) 21. 5x+2
and 3x - 4 23. 2{4v - 3){v + 5) 25. 5 (w - 2)(4w - 1) - 3(3r- 5 ){r+ 2) 29-33. Answers may vary. Samples
are given. 29. -31, (5v+ 3){3v- 8 ); 31,
(5v — 3)(3v + 8 ) 31. 20, (3g + 2)(3g + 2); 15,
(3g + 1 )(3g + 4) 33. 41, ( 8 r - 7){r + 6 ); - 5 ,
(8r-21)(r+ 2) 35. 6 x + 4 37a. (2x + 2)(x + 2);
(x + 1 )(2x + 4) b. yes c. Answers may vary. Sample:
Neither factoring is complete. Each one has a common
factor, 2. 39. 3(11k + 4)(2k + 1) 41. 28(b - 1)(/? + 2)- (11 n- 6)(5n - 2) 45. (9g - 5)(7g - 6 ) 47. 2;
explanations may vary. Sample: ax 2 + b x + c factors to
(ax + 1 )(x + c) or (ax + c)(x + 1 ) so b = ac + 1 or
b = a + c. 49.(7p - 3q)(7p + 12q) 51a. -2, -3
b. (x + 2)(x + 3) c. Answers may vary. Sample: if you
set each factor equal to 0 and solve the resulting
equations, you get the x-intercepts.
Lesson 8-7 pp. 523-528
Go t It? 1a. (x + 3 )2 b. (x - 7 )2 2. 4m - 9
3a. {v - 1 0)(v +10) b. (s - 4)(s + 4)
4a. (5d + 8)(5d - 8) b. No; 2 5d2 + 64 is not a
difference of two squares. 5a. 12(f + 2)(f - 2)
b. 3(2x + 1)2
Lesso n Ch eck 1. (y - 8)2 2. (3q + 2)2- (p + 6 )(p - 6 ) 4. 6w + 5 5. perfect-square trinomial
- perfect-square trinomial 7. difference of two squares
- In a difference of two squares, both terms are perfect
squares separated by a subtraction symbol.
Ex e r c i se s 9. (h + 4 )2 11.(d-10)2 13. (g+1)2 - (8x+7)2 17. (3n-7)2 19. (5z + 4)2
21.10r— 11 23. 5c+3 25. (a + 7)(a - 7) - (f + 5)(f - 5) 29. (m + 15)(m - 15)
- (9r + 1 )(9r - 1) 33. (8q + 9)(8q - 9)
- (3n + 20)(3n - 20) 37. 3(3w+ 2){3w-2)
- (x2)2 - (y2)2; (x - y)(x + y)(x^2 + y2)^41. Answers
may vary. Sample: Rewrite the absolute value of both
terms as squares. The factorization is the product of two
binomials. The first is the sum of square roots of the
squares. The second is the difference of the square roots
of the squares. Example 1: x 2 - 4 = (x + 2)(x - 2);
Example 2: 4y 2 - 25 = (2y + 5 )(2 y - 5) - [1] S u b tract by com bining like term s.
(49x 2 - 56x + 16) - (1 6x2 + 24x + 9) =
(49x 2 - 16x2) + (—56x - 24x) + (16 - 9) =
33x 2 - 80x + 7
[2] Factor each expression, then use the rule for factoring
the difference of two squares. (49x 2 - 56x + 1 6 ) -
(1 6x2 + 24x + 9) = (7x - 4)2 - (4x + 3)2 =
[(7x - 4) - (4x + 3)] - [(7x - 4) + (4x + 3)] =
(3x— 7)(11x— 1) = 33x 2 — 80x + 7 - 11,9 47. 14, 6 49a. Answers may vary. Sample:
x 2 + 6 x + 9 b. because the first term x 2 is a square, the
last term 3 2 is a square, and the middle term is
2(x)(3) 51. ( 8 r3 - 9)2 53. ( 6 m 2 + 7)2 55. (x 10 - 2y5)2
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