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WorksheetsAdding and Subtracting Polynomials
Total questions: 91
Worksheet time: 7hrs 3mins
Name
Class
Date
1.
(3x + 4y - 3z) - (2x - 6y + 7z)
a)
x + 10y - 10z
b)
-x +10y - 10z
c)
x -10y - 10z
d)
-x -10y - 10z
2.
Which of the following are examples of like terms?
a)
2 and 2x
b)
y3 and x3
c)
y and x
d)
-3x and 3x
3.
Add the polynomials.
(2x + 5y) + (3x - 2y)
(2x + 5y) + (3x - 2y)
a)
3x + 5y
b)
5x + 3y
c)
5x + 7y
d)
7xy + 1xy
4.
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
5.
What is the standard form of the polynomial,
9x2 + 5x + 27 + 2x3
9x2 + 5x + 27 + 2x3
a)
27 + 5x + 9x2 + 2x3
b)
9x2 + 5x + 2x3 + 27
c)
9x2 + 5x + 27 + 2x3
d)
2x3 + 9x2 + 5x + 27
6.
Find the sum.
(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
7.
Add: (3x - 2) + (3x2 + 6x)
a)
3x2 + 9x - 2
b)
6x2 + 4x
c)
3x2 + 3x - 2
d)
6x2 + 6x - 2
8.
Add: (3x2 + 2x + 1) + (2x2 - 4x - 5) + (3x - 1)
a)
5x2 + 6x - 7
b)
8x2 - 3x - 5
c)
5x2 + x - 5
d)
6x2 + 8x + 5
9.
Subtract: (2a2 + 5a + 3) -(a2 - 3a - 4)
a)
3a2 + 2a - 1
b)
a2 + 8a + 7
c)
3a2 + 8a + 7
d)
a2 + 2a - 1
10.
Combine like terms:
8x3y + 3x2y + 4xy + 5x2y + 2xy + 7x2y
a)
8x3y + 8x2y + 2xy
b)
11x3y + 15x2y + 8xy
c)
8x3y + 15x2y + 6xy
d)
23x2y + 6xy
11.
What is the perimeter of the rectangle?
a)
x²+8x-5
b)
2x²+16x-10
c)
2x²+10x-8
d)
6x-2
12.
What is the degree of the polynomial? 5x5 - 6x6 + 2
a)
1
b)
5
c)
6
d)
11
13.
Classify by number of terms:
3x3 – 6x
3x3 – 6x
a)
Monomial
b)
Binomial
c)
Trinomial
d)
4-Term Polynomial
14.
Classify by degree of polynomial:
3x3 – 6x
3x3 – 6x
a)
Constant
b)
Linear
c)
Quadratic
d)
Cubic
15.
Classify by number of terms:
2x – 9
2x – 9
a)
Monomial
b)
Binomial
c)
Trinomial
d)
4-Term Polynomial
16.
Classify by degree of polynomial:
2x – 9
2x – 9
a)
Constant
b)
Linear
c)
Quadratic
d)
Cubic
17.
Classify by number of terms:
3x2 – 8x + 1
3x2 – 8x + 1
a)
Monomial
b)
Binomial
c)
Trinomial
d)
4-Term Polynomial
18.
Classify by degree of polynomial:
3x2 – 8x + 1
3x2 – 8x + 1
a)
Constant
b)
Linear
c)
Quadratic
d)
Cubic
19.
Classify by degree of polynomial:
9x
9x
a)
Constant
b)
Linear
c)
Quadratic
d)
Cubic
20.
Classify by degree of polynomial:
7x3 – 8x2 -4x+ 9
7x3 – 8x2 -4x+ 9
a)
Constant
b)
Linear
c)
Quadratic
d)
Cubic
21.
(3x + 4y - 3z) - (2x - 6y + 7z)
a)
x + 10y - 10z
b)
-x +10y - 10z
c)
x -10y - 10z
d)
-x -10y - 10z
22.
Simplify:
a)
9n3 + 4n
b)
7n3 + 6
c)
-3n3 + 2
d)
7n6 + 6
23.
(4x3-5x2+3x)+(-2x3-x2+6x)
a)
2x3-6x2-9x
b)
2x3+6x2+9x
c)
-2x3-6x2+9x
d)
2x3-6x2+9x
24.
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
25.
Add or Subtract to Simplify:
(x + 2x2) + (4x2 + 7x)
(x + 2x2) + (4x2 + 7x)
a)
6x2 + 8x
b)
8x2 + 6x
c)
2x2 + 6x
d)
2x2 + 8x
26.
Add or Subtract to Simplify:
(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
27.
Add or Subtract to Simplify:
(5x + x2 - 4) - (4x - x2 + 6)
(5x + x2 - 4) - (4x - x2 + 6)
a)
2x2 + x + 2
b)
x + 2
c)
2x2 + x - 10
d)
x - 10
28.
Add or Subtract to Simplify:
(x5 + x3) - (6x - x3 + 6x5)
(x5 + x3) - (6x - x3 + 6x5)
a)
-5x5 + 2x3 - 6x
b)
7x5 - 6x
c)
-5x3 + 2x2 - 6x
d)
-5x5 - 6x
29.
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
30.
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
31.
Simplify:
a)
9n3 + 4n
b)
7n3 + 6
c)
-3n3 + 2
d)
7n6 + 6
32.
(4x3-5x2+3x)+(-2x3-x2+6x)
a)
2x3-6x2-9x
b)
2x3+6x2+9x
c)
-2x3-6x2+9x
d)
2x3-6x2+9x
33.
(5x4 - 4x3 - 2x2 + x - 19) - (x4 + 5x3 + 8x2 + x + 5)
a)
4x4 - 9x3 - 10x2 - 24
b)
4x4 - 9x3 - 10x2 - 2x - 24
c)
4x4 - 9x3 - 10x2 + 2x - 24
d)
-4x4 - 9x3 - 10x2 - 24
34.
Is b + 8 a monomial?
a)
yes
b)
no
35.
What is the degree of the polynomial? 5x5 - 6x6 + 2
a)
1
b)
5
c)
6
d)
11
36.
Which of the following are examples of like terms?
a)
2 and 2x
b)
y3 and x3
c)
y and x
d)
-3x and 3x
37.
Add the polynomials.
(2x + 5y) + (3x - 2y)
(2x + 5y) + (3x - 2y)
a)
3x + 5y
b)
5x + 3y
c)
5x + 7y
d)
7xy + 1xy
38.
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
39.
What is the correct name of the following:
3x + 5y2 - 3
3x + 5y2 - 3
a)
monomial
b)
binomial
c)
trinomial
d)
polynomial
40.
Simplify the expression.
(4a3 - 8a - 4a2) + (7a3 - 7 - 6a)
(4a3 - 8a - 4a2) + (7a3 - 7 - 6a)
a)
11a3 - 4a2 - 14a - 7
b)
5a3 - 4a2 - 14a - 7
c)
5a3 - 4a2 - 20a - 7
d)
5a3 - 9a2 - 20a - 7
41.
Find the difference.
(3- 2x + 2x2) - (4x -5 +3x2)
(3- 2x + 2x2) - (4x -5 +3x2)
a)
x2 + 6x + 8
b)
2x2 + 5x - 7
c)
-x2 -6x + 8
d)
-2x2 + 11x - 4
42.
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
43.
Add or Subtract to Simplify:
(4x2+ x) - (x2+ 2x)
(4x2+ x) - (x2+ 2x)
a)
3x2 - x
b)
4x2 + 2x
c)
3x2 + 3x
d)
3x2 + 2x
44.
Add or Subtract to Simplify:
(x + 2x2) + (4x2 + 7x)
(x + 2x2) + (4x2 + 7x)
a)
6x2 + 8x
b)
8x2 + 6x
c)
2x2 + 6x
d)
2x2 + 8x
45.
Simplify the expression.
(4a3 - 8a - 4a2) + (7a3 - 7 - 6a)
(4a3 - 8a - 4a2) + (7a3 - 7 - 6a)
a)
11a3 - 4a2 - 14a - 7
b)
5a3 - 4a2 - 14a - 7
c)
5a3 - 4a2 - 20a - 7
d)
5a3 - 9a2 - 20a - 7
46.
(2x + 5y - z) + (-6x - 4y + 7z)
a)
-4x2 +6y2 + 6z2
b)
4x + y + 6z
c)
-4x2 - y2 + 6z2
d)
-4x + y + 6z
47.
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
48.
Simplify each expression.
(6x + 4x4 - 3x2) + (7x4 + 5x2 + 8x)
(6x + 4x4 - 3x2) + (7x4 + 5x2 + 8x)
a)
11x4 + 2x2 + 14x
b)
16x4 + x2 + 14x
c)
11x4 + x2 + 14x
d)
11x4 + 2x2 + 10x
49.
Add or Subtract to Simplify:
(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
50.
Combine like terms to simplify:
(5x + 2) + (4x + 5)
(5x + 2) + (4x + 5)
a)
9x -7
b)
-9x-11
c)
9x+7
d)
x+7
51.
(4x2+ x) - (x2+ 2x)
a)
3x2 - x
b)
4x2 + 2x
c)
3x2 + 3x
d)
3x2 + 2x
52.
5x2+ x - x2+ 4x
a)
6x2 + 5x
b)
4x2 + 3x
c)
4x2 + 5x
d)
5x2 + 5x
53.
-7xy + x + y + x - 3xy
a)
10xy +2x + y
b)
-10xy + 2x + y
c)
-10xy + y
d)
-10xy + x + y
54.
4x2 - 3x2
a)
7x2
b)
2x2
c)
x2
d)
-7x2
55.
Simplify the expression.
-4(9 + 3x) - 4(x - 2)
-4(9 + 3x) - 4(x - 2)
a)
-16x-28
b)
-16x-44
c)
20x - 12
d)
30x - 9
56.
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
57.
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
58.
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
59.
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
60.
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
61.
What is the degree classification of this polynomial?
x²+4x-8
x²+4x-8
a)
binomial
b)
trinomial
c)
quadratic
d)
cubic
62.
What is the term classification of the following polynomial?
x³-7x²+3
x³-7x²+3
a)
monomial
b)
binomial
c)
trinomial
d)
polynomial
63.
Which is an example of a linear polynomial?
a)
x²-5
b)
6x+4
c)
5x⁵
d)
2x³-9x²
64.
Which is an example of a cubic binomial?
a)
x³+5
b)
x²+3
c)
x²+5x-6
d)
5x³
65.
What is the leading coefficient of the following polynomial?
5x²-3x+6
5x²-3x+6
a)
2
b)
-3
c)
5
d)
6
66.
Which of these has a negative leading coefficient?
a)
x²+9x-4
b)
6x-9
c)
-8x+8
d)
9x
67.
What is the classification of the following polynomial?
x²-8x+10
x²-8x+10
a)
quadratic binomial
b)
cubic trinomial
c)
linear binomial
d)
quadratic trinomial
68.
Add the following polynomials:
(x³-2x²+3)+(2x³+3x²-1)
(x³-2x²+3)+(2x³+3x²-1)
a)
3x³-2x²+3x+2
b)
3x³+x²+2
c)
3x³-5x²-2
d)
3x³-x²+1
69.
Add the following polynomials
(x³-6x²+3)+(3x³+4x-1)
(x³-6x²+3)+(3x³+4x-1)
a)
4x³-2x²+2
b)
4x³-6x²+4x+2
c)
-2x³+2x+2
d)
4x³-2x²-2
70.
Subtract the following polynomials:
(3x²-3x+2)-(x²-2x+1)
(3x²-3x+2)-(x²-2x+1)
a)
2x²+x+1
b)
2x²-5x+3
c)
2x²-x+1
d)
4x²-5x+3
71.
Subtract the following polynomials:
(2x³+6x²+4x-2)-(x³+4x²-x)
(2x³+6x²+4x-2)-(x³+4x²-x)
a)
x³+2x²+5x-2
b)
x³+10x²+3x-2
c)
3x³+2x+4x-3
d)
3x³+10x²-3x-2
72.
-7xy + x + y + x - 3xy
a)
10xy +2x + y
b)
-10xy + 2x + y
c)
-10xy + y
d)
-10xy + x + y
73.
5x2+ x - x2+ 4x
a)
6x2 + 5x
b)
4x2 + 3x
c)
4x2 + 5x
d)
5x2 + 5x
74.
(4x2+ x) - (x2+ 2x)
a)
3x2 - x
b)
4x2 + 2x
c)
3x2 + 3x
d)
3x2 + 2x
75.
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
76.
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
77.
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
78.
Classify the polynomial and give the degree:
5x3y2
5x3y2
a)
Monomial, 3
b)
Uninomial, 3
c)
Uninomial, 5
d)
Monomial, 5
79.
Classify the polynomial and give the degree:
4x2 + 2x - 1
4x2 + 2x - 1
a)
Binomial, 3
b)
Binomial, 2
c)
Trinomial, 3
d)
Trinomial, 2
80.
What is the Perimeter?
a)
3x - 3 inches
b)
6x - 6 inches
c)
3x - 6 inches
d)
6x - 3 inches
81.
What is the degree of the polynomial? 3x2 + 5xy - 4x7y
a)
7
b)
8
c)
2
d)
3
82.
Classify this polynomial by its degree and number of terms: x2 + 6
a)
Linear polynomial
b)
Quadratic trinomial
c)
Quadratic binomial
d)
Cubic binomial
83.
Classify this polynomial by its degree and number of terms: x2 + 2x + 6
a)
Linear polynomial
b)
Quadratic trinomial
c)
Quadratic binomial
d)
Cubic trinomial
84.
Classify this polynomial by its degree and number of terms: 4x3
a)
Cubic monomial
b)
Linear binomial
c)
Cubic binomial
d)
6th degree (sextic) monomial
85.
x4+2
a)
Quadratic binomial
b)
Quadratic monomial
c)
Quartic binomial
d)
Quartic trinomial
86.
9x4
a)
Quadratic polynomial
b)
Quartic monomial
c)
Quadratic monomial
d)
Cubic monomial
87.
Classify by degree of polynomial:
3x5 – 6x
a)
Constant
b)
Linear
c)
Quadratic
d)
fifth degree
88.
When a polynomial is written in standard form, the coefficient of the first term is called the _____________.
a)
Boss coefficient
b)
Leading coefficient
c)
Best coefficient
d)
Greatest common coefficient
89.
The following polynomial is written in standard form:
7x3 - 11x2 + 8x - 5
7x3 - 11x2 + 8x - 5
a)
True
b)
False
90.
The following polynomial is written in standard form:
x2 - 10x+ 8x - 5
a)
True
b)
False
91.
−9x2y4z6 Find the degree of the monomial.
a)
Degree: 10
b)
Degree: 12
c)
Degree: 6
d)
Degree: 4
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