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WorksheetsSynthetic Division Test
Total questions: 85
Worksheet time: 11hrs 36mins
Name
Class
Date
1.
(2x3 - 5x2 + 3x + 7) ÷ (x - 2)
a)
2x3 - x2 + x + 9
b)
2x2 - x + 1
c)
2x2 - x + 1 + 9/x-2
d)
2x2 - 9x - 15 - 23/x-2
2.
(2x3 + 5x2 + 9) ÷ (x + 3)
a)
2x2 - x + 3
b)
2x3 - x2 + 3x
c)
2x2 + 11x + 33 + 108/x+3
d)
2x2 - 5x + 12
3.
(3x3 - 2x2 - 7x + 6) ÷ (x + 1)
a)
3x3 - 5x2 - 2x + 8
b)
3x2 + x - 6
c)
3x2 - 5x - 2 + 8/x+1
d)
3x3 + x2 - 6x
4.
(2x3 + 7x2 - 6x - 8) ÷ (x + 4)
a)
2x2 - x - 2
b)
2x3 - x2 - 2x
c)
2x2 + 15x + 54 + 208/x+4
d)
2x3 + 15x2 + 54x + 208
5.
Let f(x) = 4x^2 -33x -27. Is k = 9 a zero of the function?
a)
yes
b)
no
6.
if f(x) = x3+8x+24, then find f(-2) using synthetic division.
a)
12
b)
8
c)
0
d)
-6
7.
if f(x) = 3x2 -9x -20, find the value of f(5) using synthetic division.
a)
0
b)
10
c)
15
d)
-7
8.
Is (x-2) a factor of f(x)= x3-8x2+14x-4?
a)
Yes, (x-2) is 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)
No, (x-2) is not a factor. There is a remainder.
9.
When p(x) = 9x4- 45x3 + 37x2 + x +2 is divided by x - 2, a student can determine the remainder by evaluating p(2). What is the value of p(2)?
a)
p(2) = 656
b)
p(2) = 652
c)
p(2) = -64
d)
p(2) = -368
10.
What should be the order of the polynomial coefficients if
(3x - 4x3 + 6x4 + 1) / (x + 3)
(3x - 4x3 + 6x4 + 1) / (x + 3)
a)
3 0 -4 6 1
b)
6 -4 3 1 0
c)
6 -4 0 3 1
d)
-6 4 0 -3 -1
11.
If you were dividing x6 + 4x3 + 2, how many 0's would you need when setting up the top row of your synthetic division?
a)
0
b)
2
c)
4
d)
6
12.
4x4+4x3-9x2-x+2 ÷ x-1
a)
4x3+8x2-7x-2
b)
4x3+19x2-x-2
c)
4x3+8x2-x-9
d)
4x3+8x2-x-2
13.
Is (x-2) a factor of f(x)= x3-8x2+14x-4?
a)
Yes, (x-2) is 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)
No, (x-2) is not a factor. There is a remainder.
14.
4x4+4x3-9x2-x+2 ÷ x-1
a)
4x3+8x2-7x-2
b)
4x3+19x2-x-2
c)
4x3+8x2-x-9
d)
4x3+8x2-x-2
15.
For synthetic division, what would be the number in the left hand box?
a)
0
b)
1
c)
2
d)
3
16.
(2x5+5x4−14x3+17x2−7x−3)÷(x−1) Is x-1 a factor of the polynomial?
a)
Yas
b)
No
17.
Evaluate 3x5−29x4+625x3+23x2−316x−10 21 at x =−67
a)
-7/5
b)
7/5
c)
5/7
d)
-5/7
18.
Let f(x) = 3x2 - 9x +2.
Is k = -3 a zero of the function?
Is k = -3 a zero of the function?
a)
yes
b)
no
19.
Let f(x) = 4x2 -33x -27. Is k = 9 a zero of the function?
a)
yes
b)
no
20.
(2x3 + 5x2 + 9) ÷ (x + 3)
a)
2x2 - x + 3
b)
2x3 - x2 + 3x
c)
2x2 + 11x + 33 + 108/x+3
d)
2x2 - 5x + 12
21.
(3x3 + 5x - 1) ÷ (x + 1)
a)
3x3 - 3x2 + 8x - 9
b)
3x2 - 3x + 8 - 9/x+1
c)
3x2 + 3x + 8 + 7/x+1
d)
3x3 + 3x2 + 8x + 7
22.
(2x3 - 5x - 7) ÷ (x - 2)
a)
2x3 - 4x2 + 3x - 13
b)
2x3 + 4x2 +3x - 1
c)
2x2 - 4x + 3 - 13/x-2
d)
2x2 + 4x + 3 - 1/x-2
23.
x3-3x2-10x+24 ÷ x+3
a)
x2-7x+5
b)
x-8
c)
x2-6x+8
d)
x+9
24.
-2x2+4x+48 ÷ x+4
a)
-2x+12
b)
2x+12
c)
-4x+9
d)
4x+9
25.
x2-6x+8 ÷ x-2
a)
x-6
b)
x-9 R=2
c)
x-4
d)
x-8 R=3
26.
Use synthetic division:
(2x3 - 5x - 7) ÷ (x - 2)
(2x3 - 5x - 7) ÷ (x - 2)
a)
2x3 - 4x2 + 3x - 13
b)
2x3 + 4x2 +3x - 1
c)
2x2 - 4x + 3 - 13/x-2
d)
2x2 + 4x + 3 - 1/x-2
27.
Use synthetic division:
(2x3 - 5x - 7) ÷ (x - 2)
(2x3 - 5x - 7) ÷ (x - 2)
a)
2x3 - 4x2 + 3x - 13
b)
2x3 + 4x2 +3x - 1
c)
2x2 - 4x + 3 - 13/x-2
d)
2x2 + 4x + 3 - 1/x-2
28.
For synthetic division, what would be the number in the left hand box?
a)
0
b)
1
c)
2
d)
3
29.
What is the proper way to write the answer for the following problem?
a)
2x3-x2-25x+12
b)
2x4-x3-25x2-12x+0
c)
2x3-x2-25x-12
d)
2x4-x3-25x2-12x-0
30.
If you are missing an exponent in your polynomial you must put a zero as a coefficient place holder for that exponent
a)
True
b)
False
31.
Classify 4x3+5x4-6
a)
Cubic trinomial
b)
Quintic trinomial
c)
Quartic trinomial
d)
Quartic binomial
32.
Classify 6x3-8x
a)
Quintic monomial
b)
Cubic binomial
c)
Cubic monomial
d)
Constant binomial
33.
Classify by degree of polynomial:
7x3 – 8x2 - 4x + 9
7x3 – 8x2 - 4x + 9
a)
Constant
b)
Linear
c)
Quadratic
d)
Cubic
34.
Classify by number of terms:
3x3 – 6x
3x3 – 6x
a)
Monomial
b)
Binomial
c)
Trinomial
d)
4-Term Polynomial
35.
(m - 5)(m+5) =
a)
m2 - 52
b)
m2 - 25
c)
Both
d)
Neither
36.
x6 - 4 =
a)
(x3 + 2)(x3 - 2)
b)
(x3 + 2)(x3 + 2)
c)
(x3 - 2)(x3 - 2)
d)
None of the above
37.
(x-4)(x+4) = x2 + 8
a)
True
b)
False; x2 + 8x + 16
c)
False; x2 + 16
d)
False; x2 - 16
38.
(a - b)2 = a2 - b2
a)
True
b)
False; a2 + b2
c)
False; a2 + 2ab + b2
d)
False; a2 -2ab + b2
39.
(a-b)(a+b) = a2 + b2
a)
True
b)
False; a2 + 2ab + b2
c)
False; a2 - b2
d)
False; a2 -2ab -b2
40.
(2h2 - k2)2
a)
4h4 - 4h2k2 + k4
b)
4h4 + 4h2k2 + k4
c)
4h4 + k4
d)
4h4 - k4
41.
(x - 4y)2
a)
X2 - 16y2
b)
X2 +8xy -16y2
c)
x2 - 8xy +16y2
d)
x2 + 4y2
42.
( 2x - 8)2
a)
4x2 + 64
b)
4x2 -16x + 64
c)
4x2 + 16x - 64
d)
4x2 - 64
43.
What should be the order of the polynomial coefficients if
(3x - 4x3 + 6x4 + 1) / (x + 3)
(3x - 4x3 + 6x4 + 1) / (x + 3)
a)
3 0 -4 6 1
b)
6 -4 3 1 0
c)
6 -4 0 3 1
d)
-6 4 0 -3 -1
44.
For synthetic division, what would be the number in the left hand box?
a)
0
b)
1
c)
2
d)
3
45.
If you were dividing x6 + 4x3 + 2, how many 0's would you need when setting up the top row of your synthetic division?
a)
0
b)
2
c)
4
d)
6
46.
Which term is missing in this problem?
2x3 + 5x2 + 9 ÷
x + 3
2x3 + 5x2 + 9 ÷
x + 3
a)
x4
b)
x3
c)
x2
d)
x
47.
(2x3 + 7x2 - 6x - 8) ÷ (x + 4)
a)
2x2 - x - 2
b)
2x3 - x2 - 2x
c)
2x2 + 15x + 54 + 208/x+4
d)
2x3 + 15x2 + 54x + 208
48.
-2x2+4x+48 ÷ x+4
a)
-2x+12
b)
2x+12
c)
-4x+9
d)
4x+9
49.
(2x3 - 5x2 + 3x + 7) ÷ (x - 2)
a)
2x3 - x2 + x + 9
b)
2x2 - x + 1
c)
2x2 - x + 1 + 9/x-2
d)
2x2 - 9x - 15 - 23/x-2
50.
Give the correct name for
2x3+5x
2x3+5x
a)
Linear Binomial
b)
Cubic Binomial
c)
Quadratic Trinomial
d)
Linear Trinomial
51.
a)
x - 7
b)
x2 - 7
c)
x + 7
d)
x2 + 3x - 54
52.
a)
2x3 + 3x + (7/x-4)
b)
2x2 + 3x + 8 + (7/x-4)
c)
2x2 + 3x + 8
d)
2x2 - x + 10 + (6/x-4)
53.
Is (x-2) a factor of f(x)= x3-8x2+14x-4?
a)
Yes, (x-2) is 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)
No, (x-2) is not a factor. There is a remainder.
54.
Divide using synthetic division
(2x³ + 4x² - 5) by (x + 3).
(2x³ + 4x² - 5) by (x + 3).
a)
2x² + 2x - 4 R(-12)
b)
2x² - 2x + 6 R(-23)
c)
2x² - 2x + 8 R(-20)
d)
2x² - 4x + 1 R0
55.
a)
x + 5 + (2/2x - 4)
b)
x - 8
c)
x - 5 + (3/2x - 4)
d)
x + 5
56.
The answer to a division problem is known as the...?
a)
product
b)
sum
c)
difference
d)
quotient
57.
What does it mean to be a factor of a number?
a)
Divides evenly with a remainder of zero.
b)
Divides unevenly with a remainder of 1.
58.
If you are missing an exponent in your polynomial you must put a zero as a coefficient place holder for that exponent
a)
True
b)
False
59.
If 𝒙2+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?
a)
0
b)
-3
c)
9
d)
5
60.
Find all the zeros, given that f(-3) = 0
f(x) = 2x3+5x2-6x-9
f(x) = 2x3+5x2-6x-9
a)
-1,-3,-3
b)
-1,-3,3/2
c)
3,3,3
d)
-3,2/3,-1
61.
When p(x) = 9x4- 45x3 + 37x2 + x +2 is divided by x - 2, a student can determine the remainder by evaluating p(2). What is the value of p(2)?
a)
p(2) = 656
b)
p(2) = 652
c)
p(2) = -64
d)
p(2) = -368
62.
What is the proper way to write the answer for the following problem?
a)
2x3-x2-25x+12
b)
2x4-x3-25x2-12x+0
c)
2x3-x2-25x-12
d)
2x4-x3-25x2-12x-0
63.
Cam divided (x4 + 3x2 - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?
a)
Cam wrote the remainder incorrectly.
b)
Cam did not use a zero place holder for the x3 term.
c)
Cam added instead of subtracting the rows.
d)
Cam should have used -2 as his division since the factor was x-2.
64.
What should be the order of the polynomial coefficients if
(3x - 4x3 + 6x4 + 1) / (x + 3)
(3x - 4x3 + 6x4 + 1) / (x + 3)
a)
3 0 -4 6 1
b)
6 -4 3 1 0
c)
6 -4 0 3 1
d)
-6 4 0 -3 -1
65.
If you were dividing x6 + 4x3 + 2, how many 0's would you need when setting up the top row of your synthetic division?
a)
0
b)
2
c)
4
d)
6
66.
(2x3 + 5x2 + 9) ÷ (x + 3)
a)
2x2 - x + 3
b)
2x3 - x2 + 3x
c)
2x2 + 11x + 33 + 108/x+3
d)
2x2 - 5x + 12
67.
(3x3 + 5x - 1) ÷ (x + 1)
a)
3x3 - 3x2 + 8x - 9
b)
3x2 - 3x + 8 - 9/x+1
c)
3x2 + 3x + 8 + 7/x+1
d)
3x3 + 3x2 + 8x + 7
68.
Use synthetic division:
(2x3 - 5x - 7) ÷ (x - 2)
(2x3 - 5x - 7) ÷ (x - 2)
a)
2x3 - 4x2 + 3x - 13
b)
2x3 + 4x2 +3x - 1
c)
2x2 - 4x + 3 - 13/x-2
d)
2x2 + 4x + 3 - 1/x-2
69.
For synthetic division, what would be the number in the left hand box?
a)
0
b)
1
c)
2
d)
3
70.
Let f(x) = 4x2 -33x -27. Is k = 9 a zero of the function?
a)
yes
b)
no
71.
If you were dividing x6 + 4x3 + 2, how many 0's would you need when setting up the top row of your synthetic division?
a)
0
b)
2
c)
4
d)
6
72.
Give the correct name for
2x3+5x
2x3+5x
a)
Linear Binomial
b)
Cubic Binomial
c)
Quadratic Trinomial
d)
Linear Trinomial
73.
If you are missing an exponent in your polynomial you must put a zero as a coefficient place holder for that exponent
a)
True
b)
False
74.
What is the proper way to write the answer for the following problem?
a)
2x3-x2-25x+12
b)
2x4-x3-25x2-12x+0
c)
2x3-x2-25x-12
d)
2x4-x3-25x2-12x-0
75.
Let f(x) = 3x2 - 9x +2.
Is k = -3 a zero of the function?
Is k = -3 a zero of the function?
a)
yes
b)
no
76.
Let f(x) = 4x2 -33x -27. Is k = 9 a zero of the function?
a)
yes
b)
no
77.
(2x3 + 5x2 + 9) ÷ (x + 3)
a)
2x2 - x + 3
b)
2x3 - x2 + 3x
c)
2x2 + 11x + 33 + 108/x+3
d)
2x2 - 5x + 12
78.
(3x3 + 5x - 1) ÷ (x + 1)
a)
3x3 - 3x2 + 8x - 9
b)
3x2 - 3x + 8 - 9/x+1
c)
3x2 + 3x + 8 + 7/x+1
d)
3x3 + 3x2 + 8x + 7
79.
(2x3 - 5x - 7) ÷ (x - 2)
a)
2x3 - 4x2 + 3x - 13
b)
2x3 + 4x2 +3x - 1
c)
2x2 - 4x + 3 - 13/x-2
d)
2x2 + 4x + 3 - 1/x-2
80.
x3-3x2-10x+24 ÷ x+3
a)
x2-7x+5
b)
x-8
c)
x2-6x+8
d)
x+9
81.
-2x2+4x+48 ÷ x+4
a)
-2x+12
b)
2x+12
c)
-4x+9
d)
4x+9
82.
x2-6x+8 ÷ x-2
a)
x-6
b)
x-9 R=2
c)
x-4
d)
x-8 R=3
83.
Use synthetic division:
(2x3 - 5x - 7) ÷ (x - 2)
(2x3 - 5x - 7) ÷ (x - 2)
a)
2x3 - 4x2 + 3x - 13
b)
2x3 + 4x2 +3x - 1
c)
2x2 - 4x + 3 - 13/x-2
d)
2x2 + 4x + 3 - 1/x-2
84.
Use synthetic division:
(2x3 - 5x - 7) ÷ (x - 2)
(2x3 - 5x - 7) ÷ (x - 2)
a)
2x3 - 4x2 + 3x - 13
b)
2x3 + 4x2 +3x - 1
c)
2x2 - 4x + 3 - 13/x-2
d)
2x2 + 4x + 3 - 1/x-2
85.
For synthetic division, what would be the number in the left hand box?
a)
0
b)
1
c)
2
d)
3
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