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Worksheets[Algebra 2] Long/Synthetic Division
Total questions: 15
Worksheet time: 28mins
Name
Class
Date
1.
a)
x - 7
b)
x2 - 7
c)
x + 7
d)
x2 + 3x - 54
2.
a)
2x3 + 3x + (7/x-4)
b)
2x2 + 3x + 8 + (7/x-4)
c)
2x2 + 3x + 8
d)
2x2 - x + 10 + (6/x-4)
3.
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.
4.
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
5.
a)
x + 5 + (2/2x - 4)
b)
x - 8
c)
x - 5 + (3/2x - 4)
d)
x + 5
6.
The answer to a division problem is known as the...?
a)
product
b)
sum
c)
difference
d)
quotient
7.
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.
8.
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
9.
If 𝒙2+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?
a)
0
b)
-3
c)
9
d)
5
10.
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
11.
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
12.
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
13.
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.
14.
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
15.
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
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