Download Answers for the lesson “Apply the Remainder and Factor Theorems”

LESSON
2.5
Answers for the lesson “Apply the Remainder
and Factor Theorems”
Skill Practice
1. If a polynomial f (x) is divided
by x 2 k, then the remainder
is r 5 f(k).
2. The red numbers are the
coefficients of the quotient and
the blue number is the remainder.
3
3. x 1 5 1 }
x24
26
4. 3x 1 4 1 }
x25
5.
6.
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
7.
8.
9.
10.
11.
9
x 1 4x 1 7 1 }
x21
8
2x 1 9 1 }
4x 2 1
24x 1 1
3x 1 8 1 }
x2 1 x
26
7x 1 11 1 }
x2 1 1
2122x 1 109
5x 2 2 12x 1 37 1 }}
x 2 1 2x 2 4
161x 1 84
4x 2 1 12x 1 44 1 }
x 2 2 3x 2 2
25
2x 1 3 1 }
x25
29
16. x 2 2 3x 1 5 1 }
x13
26
17. x3 1 x 2 2 2x 1 1 1 }
x26
10
18. x 3 2 x 2 1 5x 2 9 1 }
x15
19. The degree of the answer should
be reduced by 1;
1
.
x 2 1 2x 2 1 1 }
x22
20. The coefficient of x 2 was
not included.
2
215
12. 4x 2 5 1 }
x22
215
13. x 1 4 1 }
x14
18
14. x 1 3 1 }
x23
1
x 2 1 2x 2 1 1 }
x22
2
1
1
0
2
2
25
4
21
3
22
1
21. (x 2 6)(x 2 5)(x 1 1)
22. (x 2 1)(x 1 3)(x 1 4)
23. (x 2 8)(x 1 2)(x 1 4)
24. (x 1 3)(x 1 5)(x 1 10)
25. (x 2 4)(x 2 3)(x 1 9)
26. (x 2 6)(x 2 5)(x 1 2)
27. (2x 2 7)(x 2 3)(x 2 1)
28. (x 2 5)(3x 1 1)(x 1 4)
29. 21, 6
1
30. 24, }
4
218
15. x 2 2 x 2 4 1 }
x24
Algebra 2
Answer Transparencies for Checking Homework
66
2 3
31. 2}, }
5 2
2
32. 28, }
3
}
24 6 Ï 14
33. }
2
44. a. 40x 2 4x 3
}
11 6 Ï 41
34. }
10
c. 24 5 25x 2 4x 3, 1.386,
22.886; 1,386,000 radios
35. D
36. 2x 1 5
37. x 1 8
38. a. 23, 6
b. (x 2 6)(x 2 2)(x 1 3)
c. 23, 2, 6
39. A
40. a. 0.5
b. (x 2 0.5)(15x 2 1 11x 2 14)
c. (2x 2 1)(3x 2 2)(5x 1 7)
Problem Solving
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
b. P 5 25x 2 4x 3
41. 1 million T-shirts
42. 2 million MP3 players
43. f(x) 5 20.132x 2 1 11.2x 2
408,803
560.9 1 }
14.8x 1 725
d. No; the negative solution does
not make sense because the
company cannot produce a
negative number of radios.
45. P 5 20.0023x 3 1 0.249x 2 2
445,000
21.0x 1 1740 2 }
;
3.10x 1 256
divided the overnight stays
function by the total visits
function.
46. The only other solution is 24.
The company cannot produce a
negative number of DVDs.
Mixed Review of
Problem Solving
1. a. 1.64 3 1011
b. about 1.37 3 109 football fields
2. a. T(x) 5 8x3
b. C(x) 5 8x3 2 36x2 1
48x 2 16
c. I(x) 5 T(x) 2 C(x)
d. I(x) 5 36x 2 2 48x 1 16;
1936 in.3
Algebra 2
Answer Transparencies for Checking Homework
67
3. They will both exchange at the
same rate because they both have
a surface area-to-volume ratio
7. 4 ft;
4
6
of }x .
4. Sample answer:
f(x) 5 23x 4 1 2x 3 1 12
5. a. degree: 4, type: quartic
b. t
0
1
2
C 51 46.14 42.33
t
3
4
5
C 40.50 40.97 43.38
t
6
7
8
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
C 46.73 49.38 49.05
c. No; cell phone bills can not
be a negative amount as the
function shows after 2006.
6. a. r 5 100x 2 10x 3
b. P 5 70x 2 10x 3
c. 60 5 70x 2 10x 3; 23, 1
d. No; the manufacturer cannot
produce a negative number
of cameras.
Algebra 2
Answer Transparencies for Checking Homework
68