factorize 8x^3+5x^3+1

8x^3+5x^3+1?

13 x^3 + 1

using a³ + b³  = (a + b)(a² – ab + b²)

a=(13)^1/3x , b=1

so

13x^3 + 1 = ((13)^1/3x+1)((13)^2/3 - (13)^1/3x + 1)

Now find the roots

 roots are

x = - 1 / (13)^1/3

x = (13)^1/3+√(13)^1/2- 52*(13)^1/3

x = (13)^1/3+√(13)^1/2+ 52*(13)^1/3

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