incorrect factors found for x3+y3+x2y+y2x

[serge45]

When asking for factoring : x^3+y^3+x^2.y+y^2.x
gives : (1+xy)(x+y) (using the AC method for factoring)
which is not correct.
Same thing requesting "Factor by Grouping".
Bug ?

 

[stapel]

When asking for factoring : x^3+y^3+x^2.y+y^2.x
gives : (1+xy)(x+y) (using the AC method for factoring)
which is not correct.
Same thing requesting "Factor by Grouping".
Bug ?

I'm sorry, but this is cryptic to the point of unintelligibility. Are you saying that you're using some software package to which you suspect that many or most of us have access...? And that you're entering this non-quadratic into that software package, asking it to apply quadratic methods to its factorization, and wondering why the results aren't making sense...? And then you asking whatever software package to apply another (possibly more general) method, and you're getting something you don't like...? And you'd like us to contact the manufacturer with a "bug" report of some sort...? :shock:

 

[pka]

When asking for factoring : x^3+y^3+x^2.y+y^2.x
gives : (1+xy)(x+y) (using the AC method ?? for factoring) which is not correct.

\(\displaystyle x^3+y^3+x^2y+xy^2\\x^2(x+y)+y^2(x+y)\\(x+y)(x^2+y^2)\)

 

[Ishuda]

When asking for factoring : x^3+y^3+x^2.y+y^2.x
gives : (1+xy)(x+y) (using the AC method for factoring)
which is not correct.
Same thing requesting "Factor by Grouping".
Bug ?

The AC method that I have seen applies to a quadratic, not cubic, so we need to get around that problem. What if we re-write the expression as
x * x² + (x*y+y²) * x + y³
That is
A = x
B = x*y+y²
C = y³

BTW: I hadn't heard it called the AC method before, i had to look it up. I wonder what it was called 60-65 years ago.

 

[lookagain]

When asking for factoring : x^3+y^3+x^2.y+y^2.x
gives : (1+xy)(x+y) (using the AC method for factoring)
which is not correct.
Same thing requesting "Factor by Grouping".
Bug ?

Let's do factor by grouping different ways by associating the terms differently:


\(\displaystyle x^3 \ + \ y^3 \ + \ x^2y \ + \ y^2x \ = \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \) <The first pair is a sum of two cubes.>

\(\displaystyle (x + y)(x^2 \ - \ xy \ + \ y^2) \ + \ xy(x + y) \ = \)

\(\displaystyle (x + y)(x^2 \ - \ xy \ + \ y^2 \ + \ xy) \ = \)

\(\displaystyle \boxed{ \ (x + y)(x^2 + y^2) \ }\)


or


\(\displaystyle x^3 \ + \ x^2y \ + \ y^2x \ + \ y^3 \ = \ \)

\(\displaystyle x^2(x + y) \ + \ y^2(x + y) \ = \)

\(\displaystyle \boxed{ \ (x + y)(x^2 + y^2) \ }\)


or


\(\displaystyle x^3 \ + \ y^2x \ + \ x^2y \ + \ y^3 \ = \ \)

\(\displaystyle x(x^2 + y^2) \ + \ y(x^2 + y^2) \ = \)

\(\displaystyle \boxed{ \ (x + y)(x^2 + y^2) \ }\)

 

[serge45]

Some more explanations

When asking for factoring : x^3+y^3+x^2.y+y^2.x
gives : (1+xy)(x+y) (using the AC method for factoring)
which is not correct.
Same thing requesting "Factor by Grouping".
Bug ?

First of all, I apologize about my post missing context and more details...
I used the "factoring calculator" which is proposed by freeMATHhelp on the Calculators tab (http://www.freemathhelp.com/factoring-calculator.php).
Entering x^3+y^3+x^2.y+y^2.x and asking for factors gives a wrong answer.

As a very first time user of this site, I thought that this calculator was provided by freeMATHhelp. I probably should raise this issue to Mathway who provides this calculator instead of alerting you. I just did it, I'll keep you inform of any news coming from them.

 

[stapel]

I used the "factoring calculator" which is [furnished] by [Mathway through] FreeMathHelp on the Calculators tab:

http://www.freemathhelp.com/factoring-calculator.php

Entering x^3+y^3+x^2.y+y^2.x and asking for factors gives a wrong answer.

Ah. That's makes much more sense!

Yes, I've confirmed that the Mathway "widget" on that page does indeed return the wrong result when the expression is entered and "Factor" is selection for the "action". Thank you for dropping Mathway a line!