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#26 Re: Help Me ! » Things to know before attempting polynomial factorization ? » 2017-04-20 00:09:19

awholenumber

I haven't started working with examples , i was simply going through some general questions . i guess i should be looking for more example questions to work with

equations.png

Not sure , where to start ?

#27 Re: Help Me ! » Things to know before attempting polynomial factorization ? » 2017-04-19 23:17:05

awholenumber

Yes , i was going through this book called algebra 1 for dummies .

algebra_1_for_dummies.png

And i am somewhere around that part , Part 2 :Figuring out factoring .

and this word factoring comes up in various forms, and i am bit confused .

is it prime factoring again ?

#28 Help Me ! » Things to know before attempting polynomial factorization ? » 2017-04-19 22:43:54

awholenumber
Replies: 12

I have been learning things like these for some time now , i want to move to polynomial factorization

Prime Numbers

The first few prime numbers are 2, 3, 5, 7, 11, 13 .
A prime number is a positive integer which has no factors other than 1 and itself. 1 itself, by definition, is not a prime number.
Prime numbers cant be divided any further and thus can be thought of as the atoms of numbers.
Any number which is not prime can be written as the product of prime numbers, we simply keep dividing it into more parts until all factors are prime

84 =  2 x 2 x 3 x 7


Prime Factor

A factor that is a prime number: one of the prime numbers that, when multiplied, give the original number.

Example: The prime factors of 15 are 3 and 5 (3×5=15, and 3 and 5 are prime numbers)




Greatest common factor (GCF)

The greatest common factor, or GCF, is the greatest factor that divides two numbers. To find the GCF of two numbers:
List the prime factors of each number.
Multiply those factors both numbers have in common. If there are no common prime factors, the GCF is 1.

Least common multiple (LCM)

A common multiple is a number that is a multiple of two or more numbers. The common multiples of 3 and 4 are 0, 12, 24, ....
The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both.

Which one of these is frequently used in polynomial factorization   ?

#29 Re: Help Me ! » what is a good book to practise some basic maths ? » 2017-04-19 22:34:19

awholenumber

Thanks

#30 Re: Help Me ! » what is a good book to practise some basic maths ? » 2017-04-19 21:25:11

awholenumber

Thanks a lot for the really big answer bob bundy ,

Sometimes rearranging a few words helps me understands these stuffs a bit better .

Every number can be uniquely factored into its components, which is one of the fundamental theorems of number theory , but a prime number cannot be factored further . right ?

#31 Re: Help Me ! » what is a good book to practise some basic maths ? » 2017-04-19 19:35:07

awholenumber

Yes , sorry about the question in the middle , we posted at the same time

can i repeat that question once more , because i am trying to put it in sentence which i can understand



I mean , a number can be factored into a product of its prime .

And what exactly is a prime number ?

Its a number that can only be evenly divided by that number itself and one ?

#32 Re: Help Me ! » what is a good book to practise some basic maths ? » 2017-04-19 19:32:13

awholenumber
bob bundy wrote:
bobbym wrote:

Everything else you seem to have a good grasp of unless I missed something .

I think tonyjaa is quoting these definitions rather than showing they are understood.

If a number is not a prime number then it can be shown as a rectangular number**:

http://i.imgur.com/BjTfcHs.gif

This diagram shows that 12 is 6x2 and 3x4.  The factors of 12 are 1,2,3,4,6,12.

By splitting 12 in half you can make 2 x 6.  But 6 can be further split into 2 x 3.  If you keep trying to split a number like this, eventually you can split no more.  At that stage you have the prime factors.  Here's an example:

54   .... I know that 54 = 6 x 9.  But I know I can split these numbers too.  6 = 2 x 3   and    9 = 3 x 3   ......  so 54 = 2 x 3 x 3 x 3

It doesn't matter how you do the first split; you always end up the same.

54 = 2 x 27 = 2 x 3 x 9 = 2 x 3 x 3 x 3

or

54 = 3 x 18 = 3 x 3 x 6 = 3 x 3 x 3 x 2

** 1 is a special case.  If you decided to say that 1 is also a prime you'd get this

54 = 2 x 3 x 3 x 3 = (2 x 1) x (3 x 1) x (3 x 1) x (3 x 1) = (2 x 1 x 1 x 1 x 1 x 1) x (3 x 1 x 1 x 1 x 1 x 1) .... and so on.

So it's best to say 1 isn't prime and 1 isn't a rectangular number.

Every number can be shown to be a product of some prime numbers.

example.

855    As this ends in a '5' it must have 5 as a factor so I'll start there:

855 = 5 x 171

Now, can 171 be split further?  Notice that 1+7+1 = 9.  There's a handy rule*** that if the digits add up to a number in the 9 times table, then the number is divisible by 9.  So I'll divide 171 by 9 next.

855 = 5 x 9 x 19

Is that the end?

No, because 9 has factors.

855 = 5 x 3 x 3 x 19

Now I'm done, because all of these factors is a prime and so cannot be split any more.

I can use this to get all the factors including the non-prime ones.

5 x 3 = 15, 3 x 3 = 9,  5 x 19 = 95, 3 x 19 = 57, 5 x 3 x 3 = 45,  5 x 3 x 19 = 285,   3 x 3 x 19 = 171

So a complete list of factors is {1, 3, 5, 9, 15, 19, 45, 57, 95, 171, 285, 855}

If you can do this for any number, you'll find it very useful in all sorts of arithmetic.

** This rule for the 9 times table also works for 3 times table, but it doesn't work for the others.

Bob


Thanks for that

#33 Re: Help Me ! » what is a good book to practise some basic maths ? » 2017-04-19 19:29:42

awholenumber

I mean , a number can be factored into a product of its prime .

And what exactly is a prime number ?

Its a number that can only be evenly divided by that number itself and one ?

#34 Re: Help Me ! » what is a good book to practise some basic maths ? » 2017-04-19 19:03:46

awholenumber

Prime Numbers

The first few prime numbers are 2, 3, 5, 7, 11, 13 .
A prime number is a positive integer which has no factors other than 1 and itself. 1 itself, by definition, is not a prime number.
Prime numbers cant be divided any further and thus can be thought of as the atoms of numbers.
Any number which is not prime can be written as the product of prime numbers, we simply keep dividing it into more parts until all factors are prime

84 =  2 x 2 x 3 x 7


Prime numbers are still confusing to me .

I don't know how to put it in better words .

Prime numbers are numbers that can only be divided by one and itself without leaving a remainder ?

#35 Re: Help Me ! » what is a good book to practise some basic maths ? » 2017-04-19 08:27:08

awholenumber

Thanks

#36 Re: Help Me ! » what is a good book to practise some basic maths ? » 2017-04-19 07:24:27

awholenumber

In math does everything start with whole numbers ?

So i was only trying to divide whole numbers there ?



is this 12/5 same as 12÷5  ? in it the 12 is the numerator , 5 becomes the denominator . it other words 12 is the dividend and 5 is the divisor ... right ?

Divisibility

If we can divide a number A by a number B without remainder, we say that B is a factor or divisor of A, and that A is a multiple of B



Prime Numbers

The first few prime numbers are 2, 3, 5, 7, 11, 13 .
A prime number is a positive integer which has no factors other than 1 and itself. 1 itself, by definition, is not a prime number.
Prime numbers cant be divided any further and thus can be thought of as the atoms of numbers.
Any number which is not prime can be written as the product of prime numbers, we simply keep dividing it into more parts until all factors are prime

84 =  2 x 2 x 3 x 7





Prime Factor


A factor that is a prime number: one of the prime numbers that, when multiplied, give the original number.

Example: The prime factors of 15 are 3 and 5 (3×5=15, and 3 and 5 are prime numbers)




Greatest common factor (GCF)

The greatest common factor, or GCF, is the greatest factor that divides two numbers. To find the GCF of two numbers:
List the prime factors of each number.
Multiply those factors both numbers have in common. If there are no common prime factors, the GCF is 1.


Least common multiple (LCM)

A common multiple is a number that is a multiple of two or more numbers. The common multiples of 3 and 4 are 0, 12, 24, ....
The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both.


I wish i had a little bit more clarity on all these subjects .

#37 Re: Help Me ! » what is a good book to practise some basic maths ? » 2017-04-19 00:42:31

awholenumber

You are very right , i always used to get lost in the mathematics jargon . my own language is not English , so i have a bit of hard time understanding all the mathematics terms

i have a bunch of very silly doubts

is this 12/5 same as 12÷5  ? in it the 12 is the numerator , 5 becomes the denominator . it other words 12 is the dividend and 5 is the divisor ... right ?

#38 Re: Help Me ! » what is a good book to practise some basic maths ? » 2017-04-18 20:09:29

awholenumber

Yes i have gone through the site a couple of times , its a very good informative website .Its just that i have some starting trouble with numbers itself
I am a bit confused about these terms , numerator , denominator ,dividend , divisor , quotient , remainder
After understanding that part i thought i would try to learn about prime numbers , prime factors , prime factorization etc ...

i simply don't know how to start .

bob bundy wrote:

hi tonyjaa

Welcome to the forum.

There is a second website called http://www.mathsisfun.com/

It has many pages that teach mathematical topics.  At the bottom of each page you will find practice questions.  Also the pages are 'cross-linked' so if you come across a term you want to know more about, it is easy to find the page for that.

Hope that helps,

Bob

Thanks , i will look into it whenever i have free time

#39 Help Me ! » what is a good book to practise some basic maths ? » 2017-04-18 07:49:42

awholenumber
Replies: 17

is there a book with some basic math practise problems ?especially arithmetic and algebra ?

#40 Introductions » hello forum , i am new here :) » 2017-04-18 07:46:25

awholenumber
Replies: 2

i am trying to improve my arithmetic and algebra .

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