Monday's Math Class, a la Sirus, the Scribe

Hi! This is the Scribe post for Monday, the 29th of October.

Our POD was thus:

Simplify:


As Paint and upload image are as of yet unfathomable concepts to a mind such as my own, I will explain here.
STEP 1 is the problem stated.
STEP 2, according to PEMDAS is to go inside the brackets, [ ] and do whatever is inside them. Within that, there are parentheses, but you cannot do anything with them, so you turn to the E, or exponent. 2x^2 is equal to 2*2*x*x, or 4x^2.
STEP 3 is rephrasing 2*2*x*x as 4x^2.
STEP 4 is distributing the -3 to the 2 and the -4x^2.
STEP 5 is simplifying, as the 6's cancel out.

Now for the Lesson.

Today, most of our focus was on Prime Numbers. For those of you who were absent, or who have forgotten, a prime number is one that has ONLY TWO factors, 1 and itself. Its opposite, if you will, composite numbers, are those that have more then two factors.

One of the problems that we had to solve was to find all of the primes between 1 and 20.
The following numbers are not prime because of the number in front of it, or in front of the colon. Thanks Gabriel, for this method.

If you'll notice, we don't have to check for 4, because if it is divisible by 2, then it is divisible by 2. We don't have to check 6 because if it is divisible by 2, then it is divisible by 6, and so on.

Also, the numbers themselves are not included, as they will go into themselves 1 time.

2: 4, 6, 8 ,10, 12, 14, 16, 18, 20
3: 6, 9, 12, 15, 18
5: 10, 15, 20
7: 14

Once you cross out the numbers that are shown here, the only primes from 1 through 20 are: 3, 5, 7, 11, 13, 17, and 19. (1 is not a prime, because it only has 1 factor, itself.)

If you use the same method for 60-70, you should come up with 61 and 67, although you would use the factors of 2, 3, 5, 7, and 11. This is because no numbers within this range are divisible by 13, as it skips the whole set.

The next fun thing was Prime factorization, which is when a number is expressed as a product of primes and their exponents.

For example, the prime factorization of 10 would be 5x2, as both are prime numbers and 5x2=10.
Another is 12, which would be 2^2x3. This is because 12=2x2x3, but we can shorten that.
One can use a factor tree to find the prime factorization.
For example, let's find the Prime Factorization of 16.
16
/\
8 2
/\
4 2
/\
2 2

There was no Homework. Except for me.
The next Scribe is to be Austin. BUH BUH BUH!
ok im done.