WorksheetsRemainder theorem and factor theorem
Total questions: 14
Worksheet time: 1hrs 22mins
Name
Class
Date
1.
What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x3 - 5x2 + 2x - 10
p(x) = x3 - 5x2 + 2x - 10
a)
0
b)
2x-10
c)
-2x-10
d)
2x+10
2.
Is (x-4) a factor of (x3 +x2 -16x-16)?
a)
YES
b)
NO
3.
(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
4.
What is the remainder when a3 - 4 is divided by a+2?
a)
-2
b)
-6
c)
-12
d)
0
5.
What is the remainder of (3x3 -5x2 -4x +1) ÷ (x + 3)?
a)
-25
b)
25
c)
113
d)
-113
6.
if f(x) = 3x2 -9x -20, find the value of f(5) using synthetic division.
a)
0
b)
10
c)
15
d)
-7
7.
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
8.
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
9.
Decide if (x-3) is a factor of 3x3+10x2-x-12
a)
Yes, it is a factor!
b)
No, it is not a factor!
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.
What is the remainder of (3x3 -5x2 -4x +1) ÷ (x + 3)?
a)
-25
b)
25
c)
113
d)
-113
12.
If 𝒙2+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?
a)
0
b)
-3
c)
9
d)
5
13.
Is (x-3) a factor of
(x3 - 3x2 + 2x + 2)?
(x3 - 3x2 + 2x + 2)?
a)
Yes
b)
No
14.
Is (x-7) a factor of (x2-5x+14)?
a)
Yes
b)
No
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