Download Review - Fundamental Concepts

Fundamental Concepts
Homework: page 27 #85-94, page 78 #7-42 odd, page 16 #63-86 odd, page 57 #5-68 odds
Rules of exponents:
1. an = a * a * a * … * a
2. a0 = 1, if a ≠0.
3.
a n 
repeated n times (n is a positive integer)
1
repeated n times.
a * a * a * ... * a
4. aman = am+n
5.
am
 a mn
n
a
6. (ab)n = anbn
7.
a
an
( )n  n
b
b
8. (am)n=amn
9. Notice that all the rules above do not have addition or subtraction in them. These rules do not
apply when addition or subtraction are involved.
Simplify each of the following: page 27 #86, 92, 94
Rules of Radicals:
1.
n
a  b means bn = a
2. The principal nth root of a real number a, n≥2 integer, is
3.
n
ab  a b
4.
n
a

b
n
n
a  a if n is odd,
n
a | a | if n is even.
n
n
a
n
b
m
5. n a m  (n a )  a n
6. Notice that all the rules above do not have addition or subtraction in them. These rules do not
apply when addition or subtraction are involved.
Simplify each of the following: page 78 #12, 18, 24, 30
Fractions:
1. For addition and subtraction: find a common denominator, change each fraction so that it has
the common denominator, adjust the fractions, add-subtract, simplify.
2. For multiplication: multiply the numerators and denominators, simplify.
3. For division: invert the denominator, then multiply.
4. Again, for 2 and 3, if add or subtract is placed in the expressions, the rules must be modified.
Simplify each of the following: page 16: #68, 72, 76, 82, 86
Factoring:
1. Factor out like terms. Continue:
2. Determine if one of these rules apply:
a. x2 – a2 = (x – a)(x + a)
b. x2 + 2ax + a2 = (x + a)2
c. x2 - 2ax + a2 = (x - a)2
d. x3 – a3 =(x - a)(x2 + ax + a2)
e. x3 + a3 =(x + a)(x2 - ax + a2)
3. General form 1: x2 + bx + c
a. find two numbers d1, d2
i. such d1d2 = c
ii. d1 + d2 = b.
b. x2 + bx + c = (x + d1)(x+d2)
4. General form 2: ax2 + bx + c
a. find two numbers d1, d2
i. such d1d2 = ac
ii. d1 + d2 = b.
b. ax2 + bx + c =a x2 + d1x + d2x + c
c. Factor by grouping
Factor each of the following: page 57 #10, 20, 28, 34, 38, 40, 48, 58, 64, 68