1. Section 4.5 Factoring Sums and Difference of Powers
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2. Difference of Powers
There is a pattern when factoring differences of powers
What pattern do you notice?
1. One of the factors will always be (a-b)
2. In the other factor, powers of “a” are descending in each term, while the powers of “a” are ascending

3. Sums of Powers
Sums of powers can only be factored when the exponents are odd numbers
What pattern do you notice?
1. One of the factors will always be (a+b)
2. The powers are the same as the previous one
2. The signs in the second are alternating, +, –, +, –,….. However the last term will always be positive

4. Ie: Mersienne Prime: 2p – 1
Sums and difference of powers have a lot of applications in advanced mathematics
One simple application is inspecting large numbers to see if they are prime numbers
A lot of prime numbers are in the difference/sums of powers with a base of 2
Ie: Mersienne Prime: 2p – 1
Largest Known Prime Number: 277,232,917 – 1
Ex: Is 251–1 a prime number? If not, what are same factors?
Note: 251–1 is a difference of powers
So one of the factors is 7
Another factor would be

5. Ex: Check if any of the values below are prime numbers
Ex: Check if any of the values below are prime numbers. If not, indicate some factors:
This number is not prime and one factor would be 3
Not prime, 7 is a factor
Not prime and one factor would be 3
This one may seem like a prime number at first
However, it is actually equal to 47 x 178,481
So, not a prime number

6. Evaluate