Factorizing Expressions: 216x2y2+150x2+6y2+72xy2+360x2y+48xy+40x+8y+7

[chhitiz]

is there any way to factorize larger expressions?
i, for example wanted to factorize-
216x²y²+150x²+6y²+72xy²+360x²y+48xy+40x+8y+7

 

[CRGreathouse]

Magma says it's irreducible:

P<x,y> := PolynomialRing(IntegerRing(), 2);
Factorization(216*x^2*y^2+150*x^2+6*y^2+72*x*y^2+360*x^2*y+48*x*y+40*x+8*y+7);

[
    <216*x^2*y^2 + 360*x^2*y + 150*x^2 + 72*x*y^2 + 48*x*y + 40*x + 6*y^2 + 8*y 
        + 7, 1>
]

Total time: 0.140 seconds, Total memory usage: 7.28MB

 

[chhitiz]

i entered the code:
P<x,y> := PolynomialRing(IntegerRing(), 2);
Factorization(216*x^2*y^2+150*x^2+6*y^2+72*x*y^2+360*x^2*y+48*x*y+40*x+8*y+2);

[
<216*x^2*y^2 + 360*x^2*y + 150*x^2 + 72*x*y^2 + 48*x*y + 40*x + 6*y^2 + 8*y
+ 2, 1>
]
and got:
[
<2, 1>,
<108*x^2*y^2 + 180*x^2*y + 75*x^2 + 36*x*y^2 + 24*x*y + 20*x + 3*y^2 + 4*y +
1, 1>
]
[
<216*x^2*y^2 + 360*x^2*y + 150*x^2 + 72*x*y^2 + 48*x*y + 40*x + 6*y^2 + 8*y
+ 2, 1>
]

Total time: 0.140 seconds, Total memory usage: 7.28
even tried to put a 3 beside the Integering()(if, that is for no. of factors), to get the same result. but i know,that the above expression is:
2(6xy+5x+y+1)(18xy+15x+3y+1)
how does this work?

 

[CRGreathouse]

Only the first two lines were input. The following lines were the output I got.

 

[chhitiz]

i entered:
P<x,y> := PolynomialRing(IntegerRing(), 2);
Factorization(216*x^2*y^2+150*x^2+6*y^2+72*x*y^2+360*x^2*y+48*x*y+40*x+8*y+2);
and got:
[
<2, 1>,
<108*x^2*y^2 + 180*x^2*y + 75*x^2 + 36*x*y^2 + 24*x*y + 20*x + 3*y^2 + 4*y +
1, 1>
]

Total time: 0.140 seconds, Total memory usage: 7.28MB
whereas above expressioon is:
2(6xy+5x+y+1)(18xy+15x+3y+1)
how does this work?

 

[Chronos]

It doesnt, as i suspect you alredy knew.

 

[chhitiz]

are there more sites like the above mentioned magma?