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Expert: Sherry Wallin - 10/21/2010


Question
There are three questions that I would really appreciate help with:

1.  2^x - 2^(x-2) = 3(2^13)

   I know that the answer is x=15, but I  don't know how to get there.

2.  (1001^2 - 999^2) / (101^2 - 99^2)

    Answer = 10, I believe.

3.  How to get find the greatest prime factor of 4^17 - 2^28.

Thank you so much - I truly appreciate your help!

Answer
Christine~

Factor #1:
2^x - 2^(x-2) = 3(2^13)
2^(x-2)[2^2-1] = 3(2^13)
2^(x-2) (4-1) = 3(2^13)
2^(x-2)*3 =3*(2^13)
2^(x-2) = 2^13 =>
x-2 = 13 =>
x = 13 + 2 =>
x = 15

#2 factor, both are the difference of two square numbers
(1001^2 - 999^2)/(101^2 - 99^2) = (1001+999)(1001-999)/(101+99)(101-99)
= 2000(2)/200(2) = 2000/200 = 10

#3 factor

4^17 - 2^28 = 2^2^17-2^28 = 2^34 - 2^28 = 2^28(2^6-1) = 2^28(63)
=2^28*7*3^2 => the greatest prime would be 7

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Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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