6/5/22, 8:28 AM
Polynomial Long Division
NAME :
CLASS :
Polynomial Long Division
72 Questions
DATE :
1.
(5p2+5p-26)÷(p+3)
A
5p-12, R 1
B
5p-13, R 8
C
5p-10, R 4
D
5p-10, R 5
2.
What are the zeros of the function?
A
-2,4
B
3,1,-2,-5
C
4,1
D
-3, -1, 2, 5
3.
Expand: (a − b)5
A
a5 − 5a4 b + 10a3 b2 − 10a2 b3 + 5ab4 − b5
B
a5 − 5a4 b + 10a2 b3 − 10a3 b2 + 5ab4 − b5
C
a5 + 5a4 b + 10a3 b2 + 10a2 b3 + 5ab4 + b5
D
a5 − 5a4 b − 10a3 b2 − 10a2 b3 − 5ab4 − b5
4.
What are the three factors for
(x3 +7x2 +7x -15) ÷ (x -1)?
A
(x-1) (x+5) (x-3)
B
(x-1) (x+5) (x + 3)
C
(x+1) (x-5) (x-3)
D
(x+1) (x+5) (x-3)
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Polynomial Long Division
5.
What are the solutions to the polynomial: p(x)=(2x-1)(x2 +3x +1)
(Hint: Use quadratic formula for x2+3x+1)
A
x=1/2, (-3+√5)/2, (-3-√5)/2
B
x=-1/2, (3+√5)/2, (3-√5)/2
C
x=-1/2, (-3+√5)/2, (-3-√5)/2
D
x=1/2, (3+√5)/2, (3-√5)/2
6.
Find the zeros of the function and graph.
y=(x + 2)(x - 3)(3x - 5)
A
x=2, x=-3, x=-3/5
B
x=-2, x=3, x=5/3
C
x=2, x=-3, x=5/3
D
x=-2, x=3, x=5
A
2x2 + 3x + 8 +7/x-4
B
2x2 - 13x - 56
C
2x2 + 3x + 8 + -57/x-4
D
2x2 - 3x - 16 + -89/x-4
8.
Solve by factoring:3x2 + 5x + 2 = 0
A
x = -2/3 and x = -1
B
x = 2/3 and x = 1
C
x = -3/2 and x = -1
D
x = 2/3 and x = -1
A
Degree 7
B
Degree 6
C
Degree 5
D
Degree 3
10.
What would be the 4th term of the expansion of (a+3)4?
A
12a3
B
108a
C
81
D
27a
7.
9.
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Polynomial Long Division
11.
A
This is correct
12.
What is the next step in long division?
Put something up top, Multiply by the outside terms,
A
Add the terms
B
Subtract the terms
C
Bring the next thing down
D
Start Over
13.
Solve: 2x2-14x+24 = 0
A
x = -3, -4
B
x = 4, 3
C
x = -9/2, -10/4
D
x = 9/2, 10/4
14.
Find the sum.
(2x2 + 5x - 7) + ( 3 - 4x2 + 6x)
A
2x2 + 5x -7
B
2x2 + 3x +1
C
-2x2 - 11x -4
D
-2x2 + 11x -4
15.
What are two solutions to the polynomial:
x2+14x=0
A
x= 1, x =10
B
x=0, x= 14
C
x= -14, x = 0
D
x=-14
B
This is incorrect
16.
A
C
4x + 2
4x - 2
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B
D
4x + 2 + (1/3x - 1)
4x - 2 + (1/3x - 1)
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Polynomial Long Division
17.
What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x3 - 5x2 + 2x - 10
A
-2x-10
B
2x-10
C
0
D
2x+10
18.
Solve: 14m2-12m = 0
A
m=2 and m=76
B
m=2 and m=0
C
m=0 and m=6/7
D
m=14 and m=12
19.
What is the remainder when (48y2 + 8y + 7) ÷ (12y - 1)?
A
No remainder
B
8
C
6
D
-1
20.
Decide if (x-3) is a factor of 3x3+10x2-x-12
A
No, it is not a factor!
B
Yes, it is a factor!
21.
Is (x-2) a factor of
f(x)= x3-8x2+14x-4?
A
No, (x-2) is not a factor. There is a
remainder.
B
No, (x-2) is not a factor. The remainder is
zero.
C
Yes, (x-2) is a factor. The remainder is zero. D
Yes, (x-2) is a factor. There is a remainder.
22.
Find the difference.
(3- 2x + 2x2) - (4x -5 +3x2)
A
2x2 + 5x - 7
B
-2x2 + 11x - 4
C
-x2 -6x + 8
D
x2 + 6x + 8
23.
The solutions of the quadratic equation
x2+5x+6=0 are
A
x = -3 or x = 2
B
x = 3 or x = 2
C
x= -3 or x = -2
D
x = -6 or x = 1
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Polynomial Long Division
24.
Which standard form function matches the factored form:
y = (x + 1)(x - 3)
A
y=x-2
B
y = x2 + x - 3
C
y = x2 - 2x - 3
D
y = x2 - 2x - 2
25.
Expand
A
C
B
A
C
D
D
B
26.
Expand the expression using the Binomial Theorem.
(2x+5)4
A
2x4 + 40x3 + 300x2 + 1000x +625
C
16x4 + 1000x3 + 600x2 + 160x +625
27.
What is row 7 of Pascal's Triangle?
A
B
16x4 + 160x3 +600x2 +1000x + 625
1, 5, 10, 5, 1
B
1, 5, 10, 10, 5, 1
C
1, 7, 21, 35, 21, 7, 1
D
1, 7, 21, 35, 35, 21, 7, 1
28.
What is row 7 of Pascal's Triangle?
A
1, 7, 21, 35, 21, 7, 1
B
1, 7, 21, 35, 35, 21, 7, 1
C
1, 5, 10, 5, 1
D
1, 5, 10, 10, 5, 1
29.
Expand (d-5)5
B
d5 - 25 d4 + 250 d3 - 1250 d2 + 3125 d 3125
D
d5 + 25 d4 + 250 d3 + 1250 d2 + 3125 d +
3125
A
C
d4 + 20d3 + 150d2 + 750d + 3125
d4 - 20d3 + 150d2 - 750d + 3125
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Polynomial Long Division
30.
(v3-8v2-25v-8)÷(v+2)
A
v2-10v-5, R -2
B
v2-10v-4, R 5
C
V2-10v-5, R 2
D
v2-10v-7, R 5
31.
Select the coefficients of the 5th Row in Pascal's Triangle
A
1;3;3;1
B
1;5;10;10;5;1
C
1;4;6;4;1
D
1;6;15;20;15;6;1
32.
Choose the right Pascal's triangle
A
B
C
D
33.
Expand the expression using the Binomial Theorem.
(2x+5)4
A
2x4 + 40x3 + 300x2 + 1000x +625
C
16x4 + 1000x3 + 600x2 + 160x +625
34.
Find the product:
(y - 3)(y + 7)
A
C
B
16x4 + 160x3 +600x2 +1000x + 625
y2 + 10x - 21
B
y2 + 4y - 21
y2 - 21
D
2y - 10
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Polynomial Long Division
35.
Solve by Factoring:
x2 + 15x + 64 = 20
A
{-11}
B
{-11, -4}
C
{-8, 2}
D
{-7, 5}
36.
What are the zeros of the polynomial and state their multiplicity at each.
y = (x - 5)(x + 2)2
A
x = 5 multi 1, x = 2 multi 2
B
x = 5 multi 2, x = -2 multi 1
C
x = -5 multi 2, x = -2 multi 1
D
x = 5 multi 1, x = -2 multi 2
37.
What would be the 2nd term of the expansion of (y+4)4?
A
96y2
B
253y
C
16y3
D
64y
38.
What are the
zeros of the polynomial
y = (x + 4)(x + 1)(x - 3)?
A
3, -3, 4, 1
B
4, 1, -3
C
3, -4, -1, 3
D
-4, -1, 3
39.
According to the Fundamental Theorem of Algebra, how many solutions does the following
polynomial have?
f (x) = 13x20 − 101x + 7
A
101
B
13
C
7
D
20
40.
x + 2x2 + 3x3
is a ____
A
quadratic trinomial
B
quartic trinomial
C
quintic trinomial
D
cubic trinomial
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41.
Polynomial Long Division
Expand: (a + b)2
A
a2 + ab + b2
B
a2 − 2ab + b2
C
a2 + 2ab + b2
D
a2 − ab + b2
42.
Solve for the values of x:
(x - 3)(x + 6) = 0
A
{ 3, -6 }
B
{ -3, -6 }
C
{ -3, -6 }
D
{ 3, 6 }
43.
What are the zeros (x-intercepts)?
A
x = 2,0
B
x = 2,-2,0
C
x = 2,-2
D
x = -4,-2,2,0
44.
Solve for the values of x:
(2x - 1)(x + 4) = 0
A
{ 1/2, -4 }
B
{ 2, -4 }
C
{ -2, 4 }
D
{ 1/2, 4 }
45.
Expand
(b - 2)3
A
4b3 - 12b2 + 16b - 8
B
b3 - 2b2 + 4b - 8
C
b3 - 6b2 + 12b - 8
D
5b3 - 20b2 + 40b - 40
46.
What is the remainder when a3 - 4 is divided by a+2?
A
-12
B
0
C
-6
D
-2
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Polynomial Long Division
47.
What are the roots of the polynomial function?
y = (x + 2)(x - 7)3
A
-2, 7 multiplicity 3
B
-2, 7, 3
C
2, -7, 3
D
2, -7 multiplicity 3
48.
Use the binomial theorem to expand (4 − 2z )
3
A
64 − 64z + 144z 2 − 8z 3
B
64 − 96z + 48z 2 − 8z 3
C
64 − 96z + 48z 2 + 8z 3
D
64 + 96z + 48z 2 + 8z 3
49.
What would be the 6th term of the expansion of (m-3)5?
A
405m
B
m5
C
-243
D
-244
50.
What are the roots of the polynomial function?
y = (x + 2)(x - 7)3
A
2, -7, 3
B
-2, 7, 3
C
-2, 7 multiplicity 3
D
2, -7 multiplicity 3
51.
What should you add to this problem?
(2x3 + 5x2 + 9) ÷ (x + 3)
A
0x4
B
0x
C
0x3
D
0x2
52.
Factor the polynomial.
One zero is x = 1.
f (x) = x3 − 2x2 − 5x + 6
A
x = −1, 2, −3
B
x = 1, −2, 3
C
x = −1, −2, −3
D
x = 1, 2, 3
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Polynomial Long Division
53.
(4x2 - 24x + 35) ÷ (2x - 5)
A
2x + 12
B
2x + 7
C
2x - 7
D
2x - 12
54.
(3x3 + 5x - 1) ÷ (x + 1)
A
3x2 - 3x + 8 - 9/x+1
B
3x3 - 3x2 + 8x - 9
C
3x2 + 3x + 8 + 7/x+1
D
3x3 + 3x2 + 8x + 7
55.
Factor:
x2 + 7x - 30
A
(x + 10)(x + 3)
B
(x + 10)(x - 3)
C
(x - 10)(x + 3)
D
(x + 10)(x - 7)
56.
(2x3 - 5x - 7) ÷ (x - 2)
A
2x3 - 4x2 + 3x - 13
B
2x2 - 4x + 3 - 13/x-2
C
2x3 + 4x2 +3x - 1
D
2x2 + 4x + 3 - 1/x-2
57.
(27x3 + 9x2 - 3x - 10) ÷ (3x - 2)
A
9x2-9x+5
B
9x2+9x+5
C
9x4+5
D
9x2-9x
58.
What would be the 5th term of the expansion of (n+4)4?
A
257
B
n4
C
259
D
256
59.
What is the remainder when a3 - 4 is divided by a+2?
A
-2
B
0
C
-6
D
-12
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Polynomial Long Division
60.
A
2x + 4
B
2x - 1 + -16/4x-5
C
2x - 4
D
2x - 4 + -40/4x-5
61.
Expand (x−7)2
A
-x2 - 14x - 49
B
x2 - 14x + 49
C
49x2
D
x2 + 14x - 49
62.
If the zeros of f(x) = 5, 10, -13, then the factors of f(x) are:
A
(x - 5)(x - 10)(x - 13)
B
(x + 5)(x - 10)(x + 13)
C
(x - 5)(x - 10)(x + 13)
D
(x + 5)(x + 10)(x - 13)
63.
Factor the polynomial.
One factor is (x - 5).
f (x) = 2x3 − 9x2 − 11x + 30
A
(x + 1) (x + 2) (x − 5)
B
(2x − 3) (x + 2) (x − 5)
C
(2x − 3) (x + 2) (x + 3)
D
(x + 1) (x + 2) (x + 3)
64.
If 𝒙2+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?
A
5
B
9
C
0
D
-3
65.
Factor and solve:
0=x³+11x²+24x
A
x=0, 8, -3
B
x=-8,-3,0
C
x=8,3
D
x=-8,-3
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Polynomial Long Division
66.
3x2 - 75
A
(x+5)(x-5)
C
3( x - 5 ) ( x - 5 )
67.
What is the degree of this polynomial?
x2 + x3 + 5x6
A
B
3( x + 5 ) ( x - 5 )
2
B
5
C
3
D
6
68.
Which polynomial is written in standard form?
A
4x + x5 + x + 1
B
2x - x2
C
x3 + 5x7
D
x4 + x3 + x2
69.
What is -4x - (-17x) ?
A
13x
B
-13x
C
-21x2
D
-21x
70.
What is the Binomial expansion of (x + 1)5 ?
A
x5 + 6x4 + 15x3 + 15x2 + 6x + 1
B
x5 + 1
C
x5 + 5x4 + 15x3 + 15x2 + 5x + 1
D
x5 + 5x4 + 10x3 + 10x2 + 5x + 1
71.
What does it mean to "find the zeros"?
A
Finding the very top of the graph.
B
Finding the very bottom of the graph.
C
Finding where the graph crosses the y-axis D
72.
x2 - 16
A
( x - 8) ( x + 8)
C
( x - 4) ( x + 4)
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B
Finding where the graph crosses the x-axis
( x - 4) ( x - 4)
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Polynomial Long Division
Answer Key
1. c
2. d
3. a
4. b
5. a
6. b
7. a
8. a
9. a
10. b
11. a
12. b
13. b
14. d
15. c
16. a
17. c
18. c
19. b
20. a
21. c
22. c
23. c
24. c
25. b
26. b
27. d
28. b
29. b
30. c
31. b
32. b
33. b
34. b
35. b
36. d
37. c
38. d
39. d
40. d
41. c
42. a
43. b
44. a
45. c
46. a
47. a
48. b
49. c
50. c
51. b
52. b
53. c
54. a
55. b
56. d
57. b
58. d
59. d
60. a
61. b
62. c
63. b
64. a
65. b
66. b
67. d
68. d
69. a
70. d
71. d
72. c
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