Math 11 Unit 1 - Examples and Exercises - Mathematics 11...

Mathematics 11 Additional Exercises
DIRECTIONS: Solve the following problems completely. Show complete solutions.
A. Operations on Algebraic Expressions
Perform the following operations then simplify.
Addition and Subtraction of Polynomials
1. (4 x
3
- 7 x
2
+ 2 x - 4) + (8 x
2
+ 3 x - 7)
2. 8 y - 3 y [4 - 2( y - 1)]
3. 12 y + { [2( x - 3 y ) - 3(3 x + 4 y )] + 15 x }
Laws of Exponents
1. 4
2
· 4
3
2. ( - 2)
3
( - 2)
5
3. (7
3
)
4
4. 4
4
· 25
4
5. 9
7
· 27
5
6.
x
10
x 6
7.
y
2
y 7
8.
π
11
π
11
9.
2 m
2
3 n
3
2
10.
240 x
8
y
2
z
5
- 84 x
2
y
7
z
5
11.
8
4
x
6
y
3
z
2
2 9 x 5 yz 4
12.
2 a
3
b
- 3
c
- 1
3 a
- 2
b
- 2
c
3
3
13.
2
4
x
9
y
- 7
2 7 x - 2 y - 6
- 2
14.
a
- 1
+ b
- 1
( a + b ) - 1
Multiplication of Polynomials, Special Products
1. (3 x
2
- 2 x )( x + 1)
2. (6 x 2 - 4 x + 1)(4 - 5 x - x 2 )
3. (9 x 2 + y )(9 x 2 - y )
4. (2 x 2 - 1) 2
5. ( x - 2)
3
6. (2 a + 1)(4 a
2
- 2 a + 1)
7. 993 · 1007
Division of Polynomials
1. (6 x
3
y
2
+ 12 x
2
y
3
- 9 x
2
y
2
) ÷ (3 x
2
y
2
)
2. (2 x
2
+ 10 x
3
y - 6 xy ) ÷ 2 x
3. ( x
3
- 12 x + 20) ÷ ( x + 3)
4. ( x
3
- 7 x - x
2
+ 15) ÷ ( x + 3)
Exercises
1. (2 x + 3 x ) - [7 y + ( y - xy )]
2. x
2
+ 2 x
3
- [3 xy - (4 xy + 7 x
2
)]
3. ( x + 5)(2 x - 3)
4. ( x + 2 y - 3)(2 x + y - 5)
5. ( x
2
+ 2)
3
6. ( x
5
+ x
2
- x
3
- 1) ÷ ( x - 1)
B. Factoring