Ex e r c i se s 9. 7x 2 + 28x 11. 30m2 + 3m 3 13. 8 x 4 -
28x3 + 4x2 15.4 17.9 19.4 21. 3(3x-2)
- 7(2n 3 -5 n 2 + 4) 25. 2x(7x 2 -x + 4)
- 25x2(9 - tt) 29. -10x3 + 8x2 - 26x
- -60a3 + 20a2 - 70a 33. -t3 + t2 + t
- 2Ox2 + 5x; 5x(4 x + 1) 37. 17xy3( y + 3x)
- a5(31ab3 + 63) 41. 49; p = 7a and q = 7b, where
a and b have no common factors other than 1 , so
p 2 = 49a 2 and q2 = 49 b2. Since a 2 and b2 have no
common factors other than 1, the GCF of p 2 and q2 is - 43a. V = 64s3 b. V=48(tt)s2
c.V= 64s3 - 48(t7-)s2 d. V = 16s2(4s - 3 tt) e. about
182,088 in.3 45. 5 47. 16x5; 5 49. 8 x 2 + 4x+ 5
50. 7x 4 +3x2-1 51. -5x 3 — 6 x
52. 7x 4 + 2x 3 - 8 x 2 + 4
5 3. y < f x - 2 54. y > |x — 4
y f
I
/(^1) X
_ci—1H5- 0
f/
- y < —|rx — 3
17. 2h2 + 11 /a — 63 19.^6 p^2 + 23p + 20
21. 4x 2 + 1 1x — 20 23. b2 - 12b + 27
25. 45z 2 -7 z - 12 27. 4w 2 + 21 w + 26
29. 4-ttx 2 + 22irx + 28tt 31. x 3 + 2x 2 - 14x + 5
33. 10 a 3 + 12a 2 + 9a - 20 35. x 2 + 200x + 9375
37. -n 3 - 3n 2 - n - 3 39. 2m 3 + 10m2 + m + 5
41. 12 z 4 + 4z 3 + 3z 2 + z 43. Yes, when you multiply
two polynomials you get a sum of monomials. A sum of
monomials is always a polynomial. 45a. i. x 2 + 2x + 1,
121 ii. x 2 + 3x + 2, 132 iii. x 2 + 4 x + 3, 143
b. The digits in the product of the two integers are the
coefficients of the terms in the product of the two
binomials. 47.^6 x^2 + 24x + 24 49. 24c4 + 72c2 + 54
Lesson 8-4 pp. 504-509
Go t It? 1a. n^2 - 14n + 49 b. 4x^2 + 36x + 81
2. (16x + 64) ft 2 3a. 7225 b. Answers may vary.
Sample: You could write 85 as (80 + 5) or as (100 - 15).
4a. x^2 - 81 b. 36 - m^4 c. 9c^2 - 16 5.^2496
Lesso n Ch eck 1. c 2 + 6 c + 9 2. g2 - 8g + 16
3. 4r 2 - 9 4. 4x 2 + 12x + 9 in.2 5. The Square
of a Binomial^6. The Product of a Sum and Difference
7. The Square of a Binomial 8. Answers may vary.
Sample: You can use the rule for the product of a sum
and difference to multiply two numbers when one
number can be written as a + b and the other number
can be written as a- b.
Ex e r c i se s 9. w 2 + 10w +25 11. 9s 2 + 54s + 81
13. a2 - 1 6 a + 64 15. 25m2 - 20m + 4
17. (1 Ox + 15) units 2 19. 36-x 2 in 2 21.6241
23. 162,409 25. v 2 - 36 27. z 2 - 25 29. 100 - y 2
31.1596 33.3591 35.89,991 37. 4a 2 + 4ab + b2
39. g2 - 1 4gh + 49 h2 41. 64r2 - 80rs + 25s2
43. p 8 - 18p4p2 + 81 g 4 45. a 2 - 36b2 47. r4 - 9s 2
49. 9w 6 - z 4 5 1. 8x2 + 32x + 32
53. Answers may vary. Sample:
a 2 = b(a - b) + b2 + (a - b)2 + b(a - b) Area of
big square = sum of areas of the 4 interior rectangles
= 2b(a - b) + b2 + (a - b)2 Combine like terms.
= 2ab - 2b2 + b2 + (a - b)2 Distributive Property
= 2ab - b2 + (a - b)2 Combine like terms.
So, (a - b)2 = a 2 - 2ab + b2 by the Add. and
Subtr. Prop, of =.
55. No; ( 3 l ) 2 =(3+l) 2 =(3+l)(3+l)=3 2 +
2(3)(j) + G )2 = 9 + 3 +! = 1 2 |* 9!
57a. (3m + 1 )2 = 9m 2 + 6 m + 1 = 3(3m2 + 2m) + 1
Since 3(3m 2 + 2m) is a multiple of 3, the expression
on the right is 1 more than a multiple of 3. b. no;
(3m + 2)2 = 3(3m 2 + 4m) + 4 59. C 61. The graph
shows a line passing through (4, 0) and (0, 5). Both
sides of the graph are shaded, but there is no overlap. - 8 x - 40 57. -3 w - 12 58. 1.5c + 4
Lesson 8-3 pp. 498-503
Go t I t? 1. 4x 2 — 21 x — 18 2. 3x2 + 13x + 4
3a. 3x 2 + 2x - 8 b. 4n2 -31n + 42
c. 4p 3 - 10p 2 + 6 p - 15 4. 4t7X 2 + 20-77X + 24-77
5a. 2x 3 - 9x 2 + 10x - 3 b. Answers may vary.
Sample: Distribute the trinomial to each term of the
binomial. Then continue distributing and combining
like terms as needed.
Lesso n Ch eck 1. x 2 + 9x + 18 2. 2x 2 + x - 15 - x 3 + 5x 2 + 2x - 8 4. x 2 + 2x - 15 5. Find the sum
of the products of the FIRST terms, OUTER terms, INNER
terms, and LAST terms. 6. 3x 2 + 11x+ 8 7. The degree
of the product is the sum of the degrees of the two
polynomials.
Ex e r c i se s 9. y 2 + 5y - 24 11. c 2 - 15c + 50 - 6 x 2 + 13x — 28 15. a 2 -12 a+ 1 1