Performing Operations on Polynomials: Solving Complex Algebraic Expressions, Assignments of Algebra

The answers to a set of algebraic expressions involving polynomial operations such as addition, subtraction, multiplication, and division. Students can use these answers to check their work or understand the steps involved in solving similar problems.

Typology: Assignments

2021/2022

Uploaded on 08/01/2022

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Elementary Algebra Skill
Performing Operations on Polynomials
Perform the indicated operation(s).
1)
(
3
v
4
− 2 + 8
v
2
)
+
(
6
v
2
+ 4 − 7
v
4
)
2)
(
4
v
2
− 5 −
v
3
)
(
3 − 6
v
3
− 3
v
2
)
3)
(
2
x
4
+
x
)
+
(
7
x
− 2
x
2
)
(
4
x
− 6
x
4
+ 5
x
2
)
4)
3
x
(
x
2
− 7
x
+ 2
)
5)
(
6
n
+ 5
)(
3
n
− 5
)
6)
(
8
a
− 2
)(
3
a
2
+ 2
a
− 2
)
7)
(
3
a
+ 2
b
)(
8
a
+ 8
b
)
8)
(
8
m
2
− 2
mn
− 7
n
2
)(
6
m
+ 3
n
)
9)
(
8
b
− 7
)(
8
b
+ 7
)
10)
(
2
y
+
x
)(
2
y
x
)
11)
(
5
p
− 3
)
2
12)
(
6
x
+
y
)
2
13)
(
5
k
5
+ 5
k
4
+ 40
k
3
)
÷ 10
k
2
14)
3
k
3
m
2
+ 3
k
2
m
3
+ 2
km
8
km
15)
(
m
2
m
− 80
)
÷
(
m
− 9
)
16)
(
n
3
+ 10
n
2
+ 29
n
+ 60
)
÷
(
n
+ 7
)
17)
(
8
v
2
v
− 4
)
÷
(
8
v
− 9
)
18)
(
2
a
2
+ 13
a
+ 21
)
÷
(
2
a
+ 7
)
-1-
pf2

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Elementary Algebra Skill

Performing Operations on Polynomials

Perform the indicated operation(s).

1) ( 3 v^4 − 2 + 8 v^2 ) + ( 6 v^2 + 4 − 7 v^4 ) 2) ( 4 v^2 − 5 − v^3 ) − (3 − 6 v^3 − 3 v^2 )

3) ( 2 x^4 + x )^ + ( 7 x − 2 x^2 )^ − ( 4 x − 6 x^4 + 5 x^2 )^ 4) 3 x ( x^2 − 7 x + 2)

5) ( 6 n + 5)( 3 n − 5)^ 6) ( 8 a − 2)( 3 a^2 + 2 a − 2)

7) ( 3 a + 2 b )( 8 a + 8 b ) 8) ( 8 m^2 − 2 mn − 7 n^2 )( 6 m + 3 n )

9) ( 8 b − 7)( 8 b + 7)^ 10) ( 2 y + x )( 2 y − x )

11) ( 5 p − 3)^2 12) ( 6 x + y )^2

13) ( 5 k^5 + 5 k^4 + 40 k^3 )^ ÷ 10 k^2 14) 3 k^3 m^2 + 3 k^2 m^3 + 2 km

8 km

15) ( m^2 − m − 80) ÷ ( m − 9) 16) ( n^3 + 10 n^2 + 29 n + 60) ÷ ( n + 7)

17) ( 8 v^2 − v − 4)^ ÷ ( 8 v − 9)^ 18) ( 2 a^2 + 13 a + 21)^ ÷ ( 2 a + 7)

-1-

-2-

Answers to Performing Operations on Polynomials

  1. −4 v^4 + 14 v^2 + 2 2) 5 v^3 + 7 v^2 − 8 3) 8 x^4 − 7 x^2 + 4 x 4) 3 x^3 − 21 x^2 + 6 x
  2. 18 n^2 − 15 n − 25 6) 24 a^3 + 10 a^2 − 20 a + 4 7) 24 a^2 + 40 ab + 16 b^2
  3. 48 m^3 + 12 m^2 n − 48 mn^2 − 21 n^3 9) 64 b^2 − 49 10) 4 y^2 − x^2
  4. 25 p^2 − 30 p + 9 12) 36 x^2 + 12 xy + y^2

k^3 2

k^2 2

  • 4 k

3 k^2 m 8

3 km^2 8

  1. m + 8 −

m − 9

  1. n^2 + 3 n + 8 +

n + 7

  1. v + 1 + 5 8 v − 9

  2. a + 3