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WorksheetsPolynomial Operations Review
Total questions: 80
Worksheet time: 20hrs 0mins
Name
Class
Date
1.
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
2.
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
3.
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
4.
How many terms are in the following polynomial?
3x3 - 2y + 8x -16
3x3 - 2y + 8x -16
a)
1
b)
2
c)
4
d)
-16
5.
What is the correct name of the following:
3x + 5y2 - 3
3x + 5y2 - 3
a)
monomial
b)
binomial
c)
trinomial
d)
polynomial
6.
Find the product:
(n - 5)(n - 1)
(n - 5)(n - 1)
a)
n2 - 5n + 5
b)
n2 - 6n + 5
c)
n2 + 5
d)
n2 + 6n + 5
7.
Multiply:
(r + 7)(r − 7)
(r + 7)(r − 7)
a)
r 2 − 49
b)
r 2 + 14
c)
r 2 − 7r + 49
d)
r 2 + 7r + 49
8.
Find the product:
(3x + 2)(2x + 4)
(3x + 2)(2x + 4)
a)
6x2 + 16x + 8
b)
5x2 +11x + 6
c)
5x2 + 16x + 6
d)
6x2 + 11x + 8
9.
Simplify:
2x ( -2x -3)
2x ( -2x -3)
a)
-4x - 3
b)
x2 - 3
c)
-4x2 - 6x
d)
-4x - 6
10.
Multiply
(x2-2x+1)(x+1)
(x2-2x+1)(x+1)
a)
x3-x2-x+1
b)
x3-2x+2
c)
x3+x2+x+1
d)
x3-3x2-3x+1
11.
Multiply (p − 8)2
a)
p 2 − 16p − 64
b)
p 2 + 16p + 64
c)
p 2 − 16p − 8
d)
p 2 − 16p + 64
12.
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
13.
a)
8x4
b)
8x8
c)
6x4
d)
6x8
14.
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
15.
(x3-x2+4) - (3x3-2x2+3)
a)
-2x3-3x2+7
b)
-2x3+x2+1
c)
2x3-3x3-1
d)
4x3-3x2+7
16.
What is the correct name of the following:
3x + 5y2 - 3
a)
linear binomial
b)
linear trinomial
c)
quadratic trinomial
d)
quadratic polynomial
17.
(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
18.
(x-3)(x2+2x+7)
a)
x3-x2+x-21
b)
x3+5x+13x-21
c)
x3-3x2+7x-21
d)
x2+2x-3
19.
Classify this polynomial by its degree and number of terms: x2 + 6
a)
Linear polynomial
b)
Quadratic trinomial
c)
Quadratic binomial
d)
Cubic binomial
20.
Classify this polynomial by its degree and number of terms: x3 + 2x + 6
a)
Cubic polynomial
b)
Quadratic binomial
c)
Quadratic trinomial
d)
Cubic trinomial
21.
x4+2
a)
Quadratic binomial
b)
Quadratic monomial
c)
Quartic binomial
d)
Quartic trinomial
22.
8
a)
Constant polynomial
b)
Linear monomial
c)
Constant monomial
d)
Linear monomial with 0 terms
23.
9x4
a)
Quadratic polynomial
b)
Quartic monomial
c)
Quadratic monomial
d)
Cubic monomial
24.
Divide using synthetic division
(2x3 - 5x - 7) ÷ (x - 2)
(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
25.
Use synthetic division
a)
2x3 + 3x (7/x-4)
b)
2x2 + 3x + 8 + (7/x-4)
c)
2x2 + 3x + 8
d)
2x2 - x + 10 + (6/x-4)
26.
Divide using long division
a)
2x - 5
b)
x - 4 + (3/4x - 5)
c)
2x + 4 + (3/4x - 5)
d)
2x + 4
27.
Is (x-7) a factor of (x2-5x+14)?
a)
Yes
b)
No
28.
Simplify:
a)
9n3 + 4n
b)
7n3 + 6
c)
-3n3 + 2
d)
7n6 + 6
29.
Classify by degree of polynomial:
3x3 – 6x
3x3 – 6x
a)
Constant
b)
Linear
c)
Quadratic
d)
Cubic
30.
Classify by number of terms:
2x – 9
2x – 9
a)
Monomial
b)
Binomial
c)
Trinomial
d)
4-Term Polynomial
31.
Classify by degree of polynomial:
2x – 9
2x – 9
a)
Constant
b)
Linear
c)
Quadratic
d)
Cubic
32.
Classify by number of terms:
3x2 – 8x + 1
3x2 – 8x + 1
a)
Monomial
b)
Binomial
c)
Trinomial
d)
4-Term Polynomial
33.
For synthetic division, what would be the number in the left hand box?
a)
0
b)
1
c)
2
d)
3
34.
a)
2x3 + 3x + (7/x-4)
b)
2x2 + 3x + 8 + (7/x-4)
c)
2x2 + 3x + 8
d)
2x2 - x + 10 + (6/x-4)
35.
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
36.
(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
37.
Find the perimeter.
a)
4x - 4
b)
2x - 2
c)
6x - 15
d)
4x + 16
38.
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
39.
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
40.
Find the product:
(2x+3)2
(2x+3)2
a)
2x+3+2x+3
b)
4x2+12x+9
c)
4x2+9
d)
16x2+9
41.
What is the correct name of the following:
3x + 5y2 - 3
3x + 5y2 - 3
a)
monomial
b)
binomial
c)
trinomial
d)
polynomial
42.
Classify the polynomial
a)
Monomial
b)
Binomial
c)
Trinomial
d)
Polynomial
43.
(x3-x2+4) - (3x3-2x2+3)
a)
-2x3-3x2+7
b)
-2x3+x2+1
c)
2x3-3x3-1
d)
4x3-3x2+7
44.
Multiply (4x + 3)(x + 2)
a)
x2 + 11x + 6
b)
4x2 + 8x + 6
c)
4x2 + 3x + 6
d)
4x2 + 11x + 6
45.
Simplify:
(3x - 5) ( 4x2 - 2x - 3)
(3x - 5) ( 4x2 - 2x - 3)
a)
12x3 - 26x2 - 25x + 15
b)
12x3 - 20x2 - 5x + 15
c)
12x3 - 20x2 - 6x + 15
d)
12x3 - 26x2 + x + 15
46.
Which of the following is the coefficient for the xy3 term of the expansion (3x-2y)4?
a)
4
b)
-24
c)
-96
d)
216
47.
Find the 4th term in the expansion of (4x-3)5.
a)
5760
b)
-4320x2
c)
5760x3
d)
-4320
48.
Divide
(5n2 - 25n + 20) ÷ (n - 4)
(5n2 - 25n + 20) ÷ (n - 4)
a)
5n - 5
b)
-5n + 5
c)
-5n - 5
d)
5n + 5
49.
Find the quotient using synthetic division:
x−3−2x4+x
a)
−2x3−6x2−18x−53−x−3159
b)
−2x3−6x2−18x−53
c)
−2x3−6x2−18x−53+x−3159
d)
None of the above
50.
Divide using synthetic division
(2x3 - 5x - 7) ÷ (x - 2)
(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
51.
The base of a triangle is represented by (2x − 6) and the height by (x − 2). Which polynomial expression BEST represents the area of the triangle?
a)
x2 + 5x + 6
b)
x2 - 5x + 6
c)
x2 - 5x - 6
d)
2x2 + 10x +12
52.
Use Binomial Theorem to expand (x−2)4
a)
x4+16
b)
x4+4x3+6x2+4x+1
c)
x4+8x3+24x2+32x+16
d)
4x+8
53.
Classify by terms
a)
Monomial
b)
Binomial
c)
Trinomial
d)
Polynomial
54.
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
55.
What is the leading coefficient of the function:
f(x) = 6x2 + 4 - 3x4 + 5x - 9x3
a)
6
b)
3
c)
-3
d)
4
56.
A function with degree 3 is called
a)
constant
b)
cubic
c)
linear
d)
quadratic
57.
Multiply (2x + 3)(2x - 3)
a)
4x2 - 12x + 9
b)
4x2 + 12x - 9
c)
4x2 - 9
d)
4x2 + 9
58.
Simplify: (x - 5)2
a)
x2 - 25
b)
x2 + 25
c)
x2 - 10x + 25
d)
x2 - 5x - 25
59.
Expand the binomial (2x+3)4
a)
16x4+81
b)
x4+4x3+6x2+4x+1
c)
16x4+96x3+216x2+216x+81
d)
16x4+186x3+398x2+312x+81
60.
Simplify:
a)
35x2 - 36
b)
35x2 + 12x - 36
c)
12x2 - 72x
d)
12x2 + 2x - 12
61.
What is the degree?
a)
4
b)
6
c)
3
d)
7
62.
Simplify
a)
(1/8)x-2y2
b)
8x2y-2
c)
0
d)
1
63.
Multiply
(x2-2x+1)(x+1)
(x2-2x+1)(x+1)
a)
x3-x2-x+1
b)
x3-2x+2
c)
x3+x2+x+1
d)
x3-3x2-3x+1
64.
Simplify the expression
(x - 3)2
(x - 3)2
a)
x2 - 6x + 9
b)
x2 + 9
c)
x2 + 6x - 9
d)
x2 + 6x + 9
65.
Simplify:
(x - 7)(x + 7)
(x - 7)(x + 7)
a)
x2 + 7x - 49
b)
x2 - 7x + 49
c)
x2 - 49
d)
x2 + 49
66.
(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
67.
According to exponent rules, when we multiply powers we _______ the exponents.
a)
add
b)
subtract
c)
multiply
d)
divide
68.
x⁵⁄x³
a)
x²
b)
x
c)
1
d)
x⁸
69.
Find the product:
(5n-8)(5n+8)
(5n-8)(5n+8)
a)
25n2-64
b)
10n2
c)
5n2+16
d)
16
70.
Find the product:
(2x+3)2
(2x+3)2
a)
2x+3+2x+3
b)
4x2+12x+9
c)
4x2+9
d)
16x2+9
71.
Simplify the expression
(x - 3)2
(x - 3)2
a)
x2 - 6x + 9
b)
x2 + 9
c)
x2 + 6x - 9
d)
x2 + 6x + 9
72.
(3x − 6)(7x + 7)
a)
21x2 − 63x + 42
b)
21x2 − 21x − 42
c)
21x2 − 42
d)
21x2 + 63x + 42
73.
Find the product:
(3r-4)(7r-5)
(3r-4)(7r-5)
a)
21r2-43r+20
b)
21r+43r2+9
c)
7r+12r
d)
r+2r
74.
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
75.
Find the difference.
(7p + 4p3 - 8) - (-3p2 + 2 - 9p)
(7p + 4p3 - 8) - (-3p2 + 2 - 9p)
a)
-3p2 + 4p3 -15 + 9
b)
3p3 + 4p2 - p + 3
c)
4p3 -3p2 +16p -10
d)
4p3 +3p2 + 16p + 10
76.
Find the perimeter of the rectangle
a)
P= 10x + 2
b)
P= 12x
c)
P = 12
d)
P = 6x2 + 3x
77.
Simplify:
(3x - 5) ( 4x2 - 2x - 3)
(3x - 5) ( 4x2 - 2x - 3)
a)
12x3 - 26x2 - 25x + 15
b)
12x3 - 20x2 - 5x + 15
c)
12x3 - 20x2 - 6x + 15
d)
12x3 - 26x2 + x + 15
78.
Find the product.
a)
a2 + b2
b)
a2 - b2
c)
a2 + 2ab + b2
d)
2a + 2b
79.
Divide.
a)
3x2 - 8x + 6
b)
3x2 - 8x + 8 + -10/x-1
c)
3x2 - 2x - 2 + -4/x-1
d)
3x2 - 2x - 4
80.
A rectangle has width (2x + 3) and length (2x - 4). What is the perimeter of the rectangle?
a)
4x - 12
b)
4x - 1
c)
8x - 2
d)
4x2 - 2x - 12
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