Question

How to factor this?\[4x^4+12x^3y+4x^3−7x^2y^2+4x^2y−25x^2−48xy^3−15xy^2−25x−36y^4−18y^3 \\ +100y^2+50y\]

Answer 1

looks like this isn't homogeneous ... try putting vales of x and y ... and try getting zeros and try reducing it using fundamental theorem of algebra.

factoring it is very tough job, you might also wanna try comparing with
\[ (a_1x^4 + ... +a_4x)(b_1 y^4 + .... + b_4y) \]

Answer 2

woops!! it wasn't of that form.

Answer 3

Hmm, yes, you are right. I can expand what you wrote.

But I am too lazy to do so!

Answer 4

I think that it's of the form you wrote...

Answer 5

Oh wait, yes.

Answer 6

no ... that would give x^4 y^4

Answer 7

same here ... if I can do it then it should be easy. If it's rigorous ... then i prefer W|A

Answer 8

\[(a_1 x^2 + a_2 xy + a_3 y^2)(b_1 x^2 + b_2 xy + b_3 y^2)\]?

Answer 9

no not that either ... you need constant on one term.

Answer 10

and there needs to be separate 'x' and 'y' terms

Answer 11

maybe u can find the factoring numbers from pascal triangle or some where else it looks like a very general 4th degree polynomial factorization

Answer 12

this isn't homegeneous

Answer 13

how do u know if its homogenous?

Answer 14

Do you think it's a perfect square? Because the abs of the coefficients of \(x^4\) and \(y^4\) are perfect squares.

Answer 15

there is cube over there

Answer 16

best of luck!! I am not doing this! definitely give medal whoever does it.

Answer 17

most likely it should be of the form
\[ (a_1 x^2 + a_2 xy + a_3 y^2+a_4 x + a_5 y)(b_1 x^2 + b_2 xy + b_3 y^2 + b_4)\]
gotta go .. best of luck!!

Answer 18

Bye bye :-)

Answer 19

watcha doingg

Answer 20

is it possible to do a whole bunch of sythentic division
with (x-a) and (y-b)

Answer 21

What I got so far is that it's the product of three trinomials
(ax + by + c)(dx + ey + f)(gx + hy + i)(jx + ky + l), working on seeing if I can factor it from there :)

Answer 22

four trinomials*

Answer 23

Gonna take a month brb

Answer 24

either c or f or i or l has to be zero

Answer 25

note that there is no constant term.

Answer 26

Yeah

Answer 27

Expanding it is still a lot of work tho :P

Answer 28

good luck!! I am super busy today

Answer 29

was it one of the bernoullis that said they found an equation to solve the 4th degree polynomials or was it fermat

Answer 30

I'm so happy I bought 2 colors of pens right now

Answer 31

that reminds me i am gonna buy one of those pens for the computer then i can draw stuff on here :)

Answer 32

to solve 4th degree polynomial you use Ferrari's method (single variable).
I use pencil for math ... but i keep losing it.

Answer 33

I use frixion pens, they're erasable :3

Answer 34

yeah .. that would make things easy.

Answer 35

also you can use Wolfram mathematica to factorize the above eqaution

Answer 36

gotta concentrate on work ... see you later guys!!

Answer 37

O god why didn't I

Answer 38

if you can without it then Don't ... it's good for practice.

Answer 39

This thing is 9 lines long atm, haven't combined like terms yet

Answer 40

try putting x=0 and see what you get, and also y=0 and what you get.

Answer 41

I give up lol