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Polynomial Operations (Long and Synthetic Divisions) 3/18/20

Total questions: 30

Worksheet time: 4hrs 41mins

Name
Class
Date
1.

Classify 4x3+5x4-6

a)

Cubic trinomial

b)

Quintic trinomial

c)

Quartic trinomial

d)

Quartic binomial

2.

Classify 6x3-8x

a)

Quintic monomial

b)

Cubic binomial

c)

Cubic monomial

d)

Constant binomial

3.
Classify by degree of polynomial:
7x3 – 8x2 - 4x + 9
a)
Constant
b)
Linear
c)
Quadratic
d)
Cubic
4.
Classify by number of terms:
3x3 – 6x
a)
Monomial
b)
Binomial
c)
Trinomial
d)
4-Term Polynomial
5.

(m - 5)(m+5) =

a)

m2 - 52

b)

m2 - 25

c)

Both

d)

Neither

6.

x6 - 4 =

a)

(x3 + 2)(x3 - 2)

b)

(x3 + 2)(x3 + 2)

c)

(x3 - 2)(x3 - 2)

d)

None of the above

7.

(x-4)(x+4) = x2 + 8

a)

True

b)

False; x2 + 8x + 16

c)

False; x2 + 16

d)

False; x2 - 16

8.

(a - b)2 = a2 - b2

a)

True

b)

False; a2 + b2

c)

False; a2 + 2ab + b2

d)

False; a2 -2ab + b2

9.

(a-b)(a+b) = a2 + b2

a)

True

b)

False; a2 + 2ab + b2

c)

False; a2 - b2

d)

False; a2 -2ab -b2

10.

(2h2 - k2)2

a)

4h4 - 4h2k2 + k4

b)

4h4 + 4h2k2 + k4

c)

4h4 + k4

d)

4h4 - k4

11.

(x - 4y)2

a)

X2 - 16y2

b)

X2 +8xy -16y2

c)

x2 - 8xy +16y2

d)

x2 + 4y2

12.

( 2x - 8)2

a)

4x2 + 64

b)

4x2 -16x + 64

c)

4x2 + 16x - 64

d)

4x2 - 64

13.
What should be the order of the polynomial coefficients if
(3x - 4x3 + 6x4 + 1) / (x + 3)
a)
3   0   -4   6   1
b)
6   -4   3   1   0
c)
6   -4   0   3   1
d)
-6   4   0   -3   -1
14.
For synthetic division, what would be the number in the left hand box?
a)
0
b)
1
c)
2
d)
3
15.
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
16.
Which term is missing in this problem?
2x3 + 5x2 + 9 ÷
x + 3
a)
x4
b)
x3
c)
x2
d)
x
17.
(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
18.
-2x2+4x+48 ÷ x+4
a)
-2x+12
b)
2x+12
c)
-4x+9
d)
4x+9
19.
(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
20.
Give the correct name for 
2x3+5x
a)
Linear Binomial
b)
Cubic Binomial
c)
Quadratic Trinomial
d)
Linear Trinomial
21.

(3v2+19v-35)÷(v+8)

a)

4v-8, R 3

b)

4v-5, R 7

c)

3v-5, R 5

d)

4v-4, R 1

22.
Is this division problem worked correctly?
a)
This is correct!
b)
This is incorrect!
23.
a)

4x - 2

b)

4x + 2

c)

4x - 2 + (1/3x - 1)

d)

4x + 2 + (1/3x - 1)

24.
a)

2x - 4

b)

2x + 4

c)

2x - 1 + -16/4x-5

d)

2x - 4 + -40/4x-5

25.
Divide
(4b2 + b - 2) ÷ (4b + 5)
a)
b + 1 - 3/4b +5
b)
b - 1 + 3/4b - 5
c)
b + 1 + 3/4b + 5
d)
b - 1 + 3/4b + 5
26.
a)
This is correct
b)
This is incorrect
27.

(27x3 + 9x2 - 3x - 10) ÷ (3x - 2)

a)

9x4+5

b)

9x2+9x+5

c)

9x2-9x+5

d)

9x2-9x

28.
What is the remainder when a3 - 4 is divided by a+2? 
a)
-2
b)
-6
c)
-12
d)
0
29.

What is the remainder when (48y2 + 8y + 7) ÷ (12y - 1)?

a)

6

b)

8

c)

-1

d)

No remainder

30.
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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