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WorksheetsPolynomial Long Division & Remainder Theorem
Total questions: 15
Worksheet time: 44mins
Name
Class
Date
1.
a)
x + 5 + (2/2x - 4)
b)
x - 8
c)
x - 5 + (3/2x - 4)
d)
x + 5
2.
a)
x - 7
b)
x2 - 7
c)
x + 7
d)
x2 + 3x - 54
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.
3x3 + 5x - 1 ÷
x + 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
5.
2x3 - 5x - 7 ÷
x - 2
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
6.
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
7.
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!
8.
Is (x-3) a factor of
(x3 - 3x2 + 2x + 2)?
(x3 - 3x2 + 2x + 2)?
a)
Yes
b)
No
9.
Find all the factors of x3 -3x2 -4x +12 given that -2 is a zero.
a)
(x-2) (x+2) (x+3)
b)
(x-2) (x-2) (x+3)
c)
(x+2) (x+2) (x+3)
d)
(x-2) (x+2) (x-3)
10.
What is the remainder when a3 - 4 is divided by a+2?
a)
-2
b)
-6
c)
-12
d)
0
11.
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
12.
What are the three factors for
(x3 +7x2 +7x -15) ÷ (x -1)?
(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)
13.
What is the remainder of (3x3 -5x2 -4x +1) ÷ (x + 3)?
a)
-25
b)
25
c)
113
d)
-113
14.
Find all the real zeros of the function
f(x) = 2x3 - 19x2 + 38x + 24 given that x-4 is a factor.
f(x) = 2x3 - 19x2 + 38x + 24 given that x-4 is a factor.
a)
x = 1/2, -6
b)
x = -1/2, 6
c)
x = 4, -1/2, 6
d)
x = -4, 1/2, -6
15.
If 𝒙2+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?
a)
0
b)
-3
c)
9
d)
5
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