Mr. J. Hughes
Unit 3 - Ch. 3.1, 3.2, Ch. 4 - Summary
Prime factorization Methods: 1) factor tree
2) repeated division(by prime factors)
GCF methods :
1) rainbow diagram /list of all factors 2) Largest factor of smallest number 3)Prime factorize chart/ list
Rainbow Diagram(GCF)
Process:
1. divide by ALL whole numbers up
to square root of number
2. Sketch “rainbow” diagram.(only whole pairs)
3. Find largest factor
Largest factor of Smallest Number(GCF)
Process:
1. Find all factors of smallest number
2. Divide largest number by each factor
of smallest, starting with largest
3. When you get a whole solution. That
factor is GCF
Prime factorize chart or list (GCF)
Process: -CHART
1. Prime factorize
2. Note all common factors
3. note the fewest of common factors
in any one prime factorization.
4. Multiply factors the number of times
indicated in chart
Prime factorize chart/list (GCF)
Process: -LIST
1. Prime factorize
2. List/align factors above each other
3. choose only the factors that align (pairs)
LCM Methods:
1) list multiples
2) Check multiples of largest number
List Multiples (LCM)
Process:
ex) LCM of 24 and 18
1. List many multiples of each
2. Choose smallest common multiple
Check Multiples of Largest Number(LCM)
Process:
ex) LCM of 24 and 18
1. List multiples of largest number
2. Divide multiples by other number
until you get a whole number. Choose this multiple
3)Prime factorize chart/list
Mr. J. Hughes
Unit 3 - Ch. 3.1, 3.2, Ch. 4 - Summary
Prime factorize chart/list (LCM)
Process: -CHART
1. Prime factorize each number or polynomial
2. List all the different factors that occur
3. Note the most number of times a factor occurs in any one
factorization (DO NOT DO THE TOTAL)
4. Multiply factors the number of times indicated
in chart
Prime factorize chart/list (LCM)
Process: -LIST
1. Prime factorize
2. List/align factors above each other
3. choose all factors -**choose “pairs” once
Simplifying Radical.
A method to simplify radicals (any index)
**there are other methods. This method is related to the prime
Steps
factoring we have been doing**
1. Prime factorize the radicand
2. Count a factor the same number of times as the index, and put the factor outside radical
[ for
...count factors two times.
3. repeat step 2 until not possible
4. Simplify (multiply factors)
For
3
...count a factor three times ]
ex.1)
ex.2)
*see other methods, p. 215-217*
If a square root simplifies to a whole number then the radicand was a perfect square ( 64 is a perfect square)
If a cube root simplifies to a whole number then the radicand was a perfect cube ( 64 is a perfect cube)
Rational Numbers - numbers that can be written as a fraction {whole numbers, fractions, terminating decimals,
9 }
repeating decimals, and any number that simplifies to one of these ex.
Irrational number- numbers that cannot be written as a fraction{ continuing- non-repeating decimals, radicals that
do not simplify to a whole number ex) 2
5}
Exponent Rules:
Fractional exponents: a
m
n

n
a
m

 a
n
m
Quotient of powers:
a m  a n  a m n
m n
Power of powers:
a 
Power of product:
a
m
b
a
n r

ex) 8 
3
2
2
  2  4....or 3 8 2 
2
4
ex) 5
a b
 am 
a mr
Power of quotients:  n   nr
b
b 
64  4
1 1
1
 1
ex) 3  2  .........or   
 3
9
9
3
2
1 2
3
ex) 3  3  3
 3  27
5
3
5 3
 32  9
ex) 2  3
3
nr
ex)
1
2
5
1
2 2
2 3 
4
4
1
2
2
6
r
3
2
 
mn
mr
 8
1
n
 na)
n
1  1
n
Negative exponents: a  n   
 a
a
m
n
m n
Product of powers: a  a  a
(Fractional with numerator of 1.... a
2
3
 52  25
4
1
2
3
2
1
2
 2 2 31  2 2 3  4  3  12
1
 21 
6
52
53 125
5 
ex)  2   2  4 
6
3
81
 3
33
3 