Question

Find all quadratic factors with real coeffiecients of z^6+8

Answer 1

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We know the algebraic identity:

x³+y³ = (x+y)(x²-xy+y²)

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Now,

$z^{6}+8$

= (z²)³+2³

=(z²+2)[(z²)²-z²×2+2²]

= (z²+2)[(z²)²-2×z²×1 + 1 + 3 ]

= (z²+2)[(z²-1)² + 3 ]

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