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WorksheetsPolynomial Operations
Total questions: 28
Worksheet time: 3hrs 45mins
Name
Class
Date
1.
(2x3 + 5x2 + 9) ÷ (x + 3)
a)
2x2 - x + 3
b)
2x3 - x2 + 3x
c)
2x2 + 11x + 33 + 108/x+3
d)
2x2 - 5x + 12
2.
(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
3.
(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
4.
x3-3x2-10x+24 ÷ x+3
a)
x2-7x+5
b)
x-8
c)
x2-6x+8
d)
x+9
5.
-2x2+4x+48 ÷ x+4
a)
-2x+12
b)
2x+12
c)
-4x+9
d)
4x+9
6.
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.
7.
(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
8.
(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
9.
(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
10.
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
11.
(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
12.
x2-6x+8 ÷ x-2
a)
x-6
b)
x-9 R=2
c)
x-4
d)
x-8 R=3
13.
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
14.
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
15.
Simplify each expression.
(4n4 - 8n + 4) - (8n2 + 4n4 + 1)
(4n4 - 8n + 4) - (8n2 + 4n4 + 1)
a)
-8n2 - 8n + 3
b)
-7n2 - 8n + 3
c)
-6n2 - 8n + 3
d)
-7n2 - 4n + 3
16.
Find the sum.
(3y2 + y3 - 5) + (4y2 -4y + 2y3 + 8)
(3y2 + y3 - 5) + (4y2 -4y + 2y3 + 8)
a)
3y3 + 7y2 - 4y + 3
b)
4y2 + 3y3 - y + 3
c)
-y4 + 2y3 -y - 4
d)
4y3 + 3y2 -3y + 1
17.
Simplify each expression.
(6b3 + 6 - b4) - (8b3 - 6b4 + 2)
(6b3 + 6 - b4) - (8b3 - 6b4 + 2)
a)
4b4 - 2b3 + 7
b)
5b4 - 2b3 + 4
c)
b4 - 2b3 + 7
d)
5b4 - 2b3 + 7
18.
Find the sum.
(2x2 + 5x - 7) + ( 3 - 4x2 + 6x)
(2x2 + 5x - 7) + ( 3 - 4x2 + 6x)
a)
2x2 + 3x +1
b)
-2x2 - 11x -4
c)
2x2 + 5x -7
d)
-2x2 + 11x -4
19.
Simplify the expression.
(4n4 - 8n + 4) - (8n2 + 4n4 + 1)
(4n4 - 8n + 4) - (8n2 + 4n4 + 1)
a)
-8n2 - 8n + 3
b)
-7n2 - 8n + 3
c)
-6n2 - 8n + 3
d)
-7n2 - 4n + 3
20.
Simplify each expression.
(6b3 + 6 - b4) - (8b3 - 6b4 + 2)
(6b3 + 6 - b4) - (8b3 - 6b4 + 2)
a)
4b4 - 2b3 + 7
b)
5b4 - 2b3 + 4
c)
b4 - 2b3 + 7
d)
5b4 - 2b3 + 7
21.
Add the polynomials.
(3x3 + 3x2 – 4x + 5) + (x3 – 2x2 + x – 4)
(3x3 + 3x2 – 4x + 5) + (x3 – 2x2 + x – 4)
a)
4x3 + 1x2 – 3x + 1
b)
2x3 + 1x2 - 5x + 9
c)
6x3 + 1x - 1x2 - 3
d)
3x5 +1x - 1x5 - 3x
22.
(2x-1)(x+5)
a)
2x2+9x−5
b)
2x+5x−1x
c)
2x2−1x+5
23.
(2x-9)(2x+4)
a)
4x2+4x+4
b)
2x2−9x+4
c)
4x2−10x−36
24.
Find the product:
(2x+3)2
(2x+3)2
a)
2x+3+2x+3
b)
4x2+12x+9
c)
4x2+9
d)
16x2+9
25.
(5x+2)(x2-3x+6)
a)
5x3 - 17x2 +24x +12
b)
5x3 + 17x2 - 24x +12
c)
5x3 - 13x2 + 24x +12
d)
5x3 +13x2 - 24x - 12
26.
(x-3)(x2+2x+7)
a)
x3-x2+x-21
b)
x3+5x+13x-21
c)
x3-3x2+7x-21
d)
x2+2x-3
27.
(5x+2y)(x2-3xy+6)
a)
5x3 - 17x2 y - 6xy2 -30x +12y
b)
5x3 + 17x2y -6xy2 - 30x +12y
c)
5x3 - 13x2y -6xy2 + 30x +12y
d)
5x3 +13x2y - 6xy - 30x + 12y
28.
Simplify the expression.
-3x2( 7x2 - x + 4)
-3x2( 7x2 - x + 4)
a)
-21x4 + 3x3 -12x2
b)
7x2 - x + 4 (-3x2)
c)
21x4 + 3x3 + 12x2
d)
-12x2 + 3x3 -21x4
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