Exam 1 Review Math 150
Jennifer Lewis
Vocabulary
Linear expression, linear factor
Irreducible quadratic
Degree of a polynomial
Leading term of a polynomial
Coefficient
Domain
Basic Facts
a  b  ( a  b )( a  b )
2
2
( a  b )  a  2 ab  b
2
2
2
a  b  ( a  b )( a  ab  b )
3
3
2
2
a  b  ( a  b )( a  ab  b )
3
3
2
2
( a  bi )( c  di )  ac  bd  ( ad  bc ) i
i  1
2
| a  bi |
a b
2
2
Know all exponent rules.
An expression is undefined if the denominator is 0.
An even root of a negative number is undefined in real numbers and is imaginary.
n
x
m
| x |
m n
when m and n are both even.
1. Write in the form
4
a)
b
ax or a | x |
243 x
128 x
28 x
whichever is appropriate.
6
b)
2
54 x
3
16 x
x
c)
b
x
d)
3
 15
6
2
3
( 2 x ) (3 x )
4
2. Find each product.
a)
( 4 x  2 )( 4 x  2 )
c)
( 2 x  7 )( 2 x  7 )
( 4 x  5 )( 2 x  3 )
b)
(2 x  7)
d)
2
3. Simplify as much as possible. Where is the expression not defined?
a)
x
( x  4)
2

x2
b)
( x  3 ) ( x  16 x )
3
x 4
2
x  5x  6
2

x  27
3
4. Simplify as much as possible.
a)
3
 54 
6
576
1
b)
27 
48 
2
5. Rationalize the denominator.
1
a)
x
6. Write in the form
a)
2
3
1
y
ab
ct
t 1
t2
1
b)
( 4 x  5 )( 4 x  5 )
2x
.
2
b)
1
c)
t
e (e )
e
t 1
3
1
c)
3
t
72 ( 5 )
7. Write in standard polynomial form. (Multiply out and put powers in decreasing order.)
a)
( 3 x  2 )( 6 x  4 )  ( 2 x  5 )
b)
( 2 x  1) ( 2 x  1)
c)
( x  4)
d)
( x  4 )( x  4 x  16 )
2
2
2
3
2
8. Divide using long division.
x  64
3
a)
3
b)
x4
2
x3
x  2x  4x  4
5
c)
x  8 x  8 x  21
3
2
x 1
2
9. Find the domain and simplify.
x  7 x  12
x 9
2
a)
x x
3
2

x  5x  6x
3
2

x 8   x3 
 2
  2

x

4
x

5
x

x

6




3
b)
10. Simplify
f ( x  h)  f ( x)
a)
h
2
f ( x)  x
c)
f ( x) 
1
x
b)
d)
for
f ( x)  x
f ( x) 
3
1
x
2
11. Evaluate each.
a)
7  2i
3  2i
b)
12. Multiply and write as a + bi.
a)
( 4  2 i )( 3  i )
c)
(1  3 i )
2
b)
d)
( 4  i )( 4  i )
( 2  6 i )( 7  3 i )
13. For each equation, find all solutions or state none exist.
a)
x  3x  2  0
b)
x  5x  2  0
c)
4 x  7 x  12  2 x  5 x  32
d)
2
2
2
1
x
e)
2
2

x
(3 x )
f)
2
1
x4

x
( x  1)
2x  4 1 
2
x2
14. Find the solution set for each inequality. Write the solution in interval form.
a)
c)
2  3x  7  5
3x  2  4
x 1
b)
d)
5 x  20  15
( x  1)
( x  1) ( x  5 )
3
2
0
x ( x  8 x  12 )
2
2
e)
2
( x  9)
2
0
f)
4
( x  2 ) ( x  25 )
3
2
0