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#1 2017-04-19 22:43:54

tonyjaa
Member
Registered: 2017-04-18
Posts: 24

Things to know before attempting polynomial factorization ?

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   ?

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#2 2017-04-19 22:52:43

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,418

Re: Things to know before attempting polynomial factorization ?

Hi;

You mean you want to factor a polynomial? Can you provide an example of what you mean?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2017-04-19 23:17:05

tonyjaa
Member
Registered: 2017-04-18
Posts: 24

Re: Things to know before attempting polynomial factorization ?

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 ?

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#4 2017-04-19 23:19:37

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,418

Re: Things to know before attempting polynomial factorization ?

Can you copy the problem so that I can see what you are dealing with?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#5 2017-04-20 00:09:19

tonyjaa
Member
Registered: 2017-04-18
Posts: 24

Re: Things to know before attempting polynomial factorization ?

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 ?

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#6 2017-04-20 00:13:13

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,918

Re: Things to know before attempting polynomial factorization ?

hi tonyjaa

If {something} times {another_something} = {yet_another_something}  then  {something} and {another_something} are factors of {yet_another_something}

eg. We know that 2 x 6 = 12.  2 and 6 are factors of 12.

In your other post about primes we looked at lots of number factors.  In your algebra book you are going to look at algebraic factors

... stuff like 2y + 6z = 2 times (y + 3z)

This started with two things added together and has landed up with two things multiplied together.  That is what algebraic factorisation is about.  You'll notice it is in part II.  I think you need to do part I first.  Then it'll be easier.

Bob

EDIT AFTER I READ YOUR POST:

There's a great way to learn about solving equations here:

http://www.mathsisfun.com/algebra/add-s … lance.html

Last edited by bob bundy (2017-04-20 00:18:29)


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#7 2017-04-20 00:29:31

tonyjaa
Member
Registered: 2017-04-18
Posts: 24

Re: Things to know before attempting polynomial factorization ?

That is a very helpful post bob bundy ,

This part was a bit confusing .

In your other post about primes we looked at lots of number factors. 
In your algebra book you are going to look at algebraic factors


I found this somewhere else ,

Factoring and Roots of Polynomials

What is factoring?

If you write a polynomial as the product of two or more polynomials, you have factored the polynomial.

Here is an example:

algebraic_factors.png

I am looking for ways to improve these factoring techniques .
I am not sure how to improve this part .

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#8 2017-04-20 00:40:44

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,918

Re: Things to know before attempting polynomial factorization ?

hi tonyjaa,

I don't want to be discouraging but are you familiar with the expression "trying to run before you can walk" ?

We can get to that example eventually, but there's a lot to do first.

How much algebra have you done already?  Please post an example of what you can do.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#9 2017-04-20 00:55:14

tonyjaa
Member
Registered: 2017-04-18
Posts: 24

Re: Things to know before attempting polynomial factorization ?

I don't know much algebra , i am just beginning . Why i am trying to refresh my algebra is that because i found this book called , Practical algebra - A self teaching guide .

I will do one thing , this looks like a right time to go through the whole book .

I will come back and ask more doubts once i finish that book properly

Thanks for the help and explanations

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#10 2017-04-20 02:50:29

tonyjaa
Member
Registered: 2017-04-18
Posts: 24

Re: Things to know before attempting polynomial factorization ?

Just a bit of an update , before i go back to the texts ...

If you write a polynomial as the product of two or more polynomials, you have factored the polynomial.

equations.png

Here is an example:

algebraic_factors.png

how do i factor a polynomial ?

factoring_quadratic_equation.png

can somebody explain this step in detail ?

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#11 2017-04-20 03:26:17

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,418

Re: Things to know before attempting polynomial factorization ?

Looks like he tried 1 x 6 and 2 x 3 for factors of 6 and then did the same thing for 15.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#12 2017-04-20 05:45:18

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,918

Re: Things to know before attempting polynomial factorization ?

hi tonyjaa,

There are two skills at work here: (1) having a pair of brackets and multiplying them to get a sum of terms and (2) reversing this by starting with the (quadratic) expression and putting it back into brackets as a pair of factors.  I think it is easier to learn to do (1) before (2)

You'll find (1) here: http://www.mathsisfun.com/algebra/polyn … lying.html

So how do we get 6x² + 19x + 15 back into brackets.

Here's a diagram for this:

ICr1c1L.gif

6x² could have come from 1x times 6x or from 2x times 3x.

15 could have come from 1 times 15 or from 3 times 5.

Only the correct choices above will give the correct middle term of 19x.  I quickly try out all the combinations to see which works.

Bob

ps.  You'll notice I wrote 'times' rather than use a cross: 'x'.  Unfortunately mathematicians like using 'x' for an unknown amount, and also as the multiplication sign.  This could lead to confusion.  So in algebraic expressions the multiply sign is often left out completely.  This is why 2 times x is written as 2x.  No times sign at all.

And 6 times x times x is written as 6x² (say: six ex squared)


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#13 2017-04-20 06:41:06

tonyjaa
Member
Registered: 2017-04-18
Posts: 24

Re: Things to know before attempting polynomial factorization ?

Thanks again for a really nice explanation bob bundy ,

I have to read this a couple of times and reading a few texts should help me .

Its so nice to finally have a grasp of all the necessary fundamentals before i can delve a bit more deep into this subject

All these information should be very helpful in the future

Thanks

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