Section 4.5 Factoring Sums and Difference of Powers © Copyright all rights reserved to Homework depot: www.BCMath.ca

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

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

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 131071

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

Evaluate