What's a proper single method to factorize all polynomials?

1. Find a root.
2. Do long division by (x-root) and go back to 1.

Works numerically on large degrees too, but you have to be more careful.

For Galois fields you move to a higher order field first.

>>8667372
how bout synthetic division?

File: 1485307388155.jpg (60KB, 650x1047px) Image search: [Google]

60KB, 650x1047px

>>8667379
have this picture then.

>>8667382
A deals a deal so I'll guess I'll tell you one safe way. I want some yuri though next time.

You could always do iteration or the numerical method. That means inputting numbers to get a close zero answer for the solution.
But that yet isn't a reliable method, because a number could be anything, or we couldn't find all roots. I get that this isn't ideal, but theres an answer.
Calculus usually sorts out the problems, by creating a simpler equation and letting you solve that and finding the intervals of high and low where in between we find a zero solution.

File: nge__just_kiss_me__by_mokuyo-d7cidr3.jpg (167KB, 1024x683px) Image search: [Google]

167KB, 1024x683px

>>8667407
does synthetic division can be used as a reliable method?

File: polynomials.jpg (151KB, 675x413px) Image search: [Google]

151KB, 675x413px

>>8667377
COUNT THE NUMBER OF TERMS

>2 terms
see pic

>3 terms
see pic

>4 terms
factor by grouping

>more than 4 terms
This is where synthetic division comes in >>8667377

>>8667417
thanks bro.

my head hurts after spending time listening all the diferent BS rules to factorize a polynomial.

>>8667346
Well for polynomials of degrees 2, 3, and 4, there's a formula that can factor all of them just by plugging in coefficients. After that idk, there are plenty of 5+ degree polynomials that can't be solved by any algebraic means.

>>8667421
the "rules" are easy to remember, since they are just based on how many terms there are

you technically COULD use synthetic division for every single proplem, but that's fucking retarded and making more work for yourself, why would you do that when for less than 4 terms the other ways are easier

>>8667424
there's like four or three ways to factorize a trinomial.

So:
two terms:
diference of squares, right?
(what if they're a sum rather than a substraction?)

three terms:
trinomial perfect.
(which is the easiest one?)

four terms:
factor by grouping.

five terms or more:
synthetic division.

is this correct?

>>8667431
>what if they're a sum rather than a substraction?
if it's a sum then you don't even need a formula to solve it. it would factor easily without any tricks.

>which is the easiest one
it depends on how the problem is written. that's why there are three different ones

>4 terms factor by grouping
correct

>5 terms of more synthetic division
correct

I actually have a better flowchart that explains everything perfectly as I had to do a refresher on that stuff last semester, ill see if I can find it

>>8667450
alright well good luck, also i lost that flowchart so you're on your own

gg

>>8667461
no, now all makes sense.

all the diferent rules makes sense for the number of monomials in the polynomials.

I was confused and thinking about doing factor by grouping to 5 or 6th grade polynomials.

or doing diference of square to trinomials.

>>8667466
Yeah that was the big epiphany for me too, they give you all these ways to do it and you're confused on which one applies to which, because they never fucking tell you that all you have to do is look at the grade of the polynomial

>>8667471
yeah man, math isn't hard, just that the teachers sucks.

Factor in C and then come back to R?