# Facorization: x^6+5*x^3+8

2
by banki

2015-04-21T01:28:37+05:30

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Let x^3 = y

y^2  + 5 y + 8
let us find roots of    y^2 + 5 y + 8 = 0
discriminant :     squareroot(25 - 40) ]
as the discriminant is negative, there are no real roots.
The given expression canno t be  factorized with real  factors.

y1 = [- 5 + √15 i ] / 2              y2 = [ -5 - √15 ] / 2
are the solutions which involve imaginary numbers.

x⁶ + 5 x³ + 8  =     (2 x³ + 5 - √15 i) (2x³ + 5 - √15 i) / 4

2015-04-21T05:54:19+05:30

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This polynomial is specially made for using the identity

With the idea of using above identity, split the middle term  as :