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For how many intergers n with |n| <500 can the polynomial Pn (x)=x6+n be written as a product of non-constant polynomisld with integer coefficients?

Guest May 13, 2015

Best Answer 

 #1
avatar+78557 
+9

x^6 + n where n is an integer,  can be factored into products of non-constant polynomials whenever n is a positive or negative perfect cube.....

Thus....... ±1,±8, ±27, ±64,  ±125,  ±216, ±343  

So.....fourteen integers

 

  

CPhill  May 13, 2015
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2+0 Answers

 #1
avatar+78557 
+9
Best Answer

x^6 + n where n is an integer,  can be factored into products of non-constant polynomials whenever n is a positive or negative perfect cube.....

Thus....... ±1,±8, ±27, ±64,  ±125,  ±216, ±343  

So.....fourteen integers

 

  

CPhill  May 13, 2015
 #2
avatar+90970 
-1

Would you like to expand on this Chris?

Melody  May 13, 2015

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