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how do I separate x^4 + y^6 into prime factors

 Oct 30, 2014

Best Answer 

 #2
avatar+128731 
+5

We can actually use a trick here to factor this as a sum of cubes.

x^4 + y^6   =  (x^4/3)^3 + (y^2)^3....so we have

[x^(4/3) + y^(2)] [x^(8/3) - x^(4/3)y^(2) + y^(4)]

However, the first term could also be factored as a sum of cubes......and we could probably continue this process forever!!!!

 

 Oct 30, 2014
 #1
avatar+23247 
+5

If you can use only real numbers, it has no factors; there are factors over the complex numbers.

Do you need it factored over the complex numbers?

 Oct 30, 2014
 #2
avatar+128731 
+5
Best Answer

We can actually use a trick here to factor this as a sum of cubes.

x^4 + y^6   =  (x^4/3)^3 + (y^2)^3....so we have

[x^(4/3) + y^(2)] [x^(8/3) - x^(4/3)y^(2) + y^(4)]

However, the first term could also be factored as a sum of cubes......and we could probably continue this process forever!!!!

 

CPhill Oct 30, 2014

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