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= (x)6+ 5x3 + 8 + x3- x3 = x6+ 6x3+ 8 - x3
[By adding and subtracting x3 on both sides]
= (x2)3+ (2)3+ (-x)3 - 3 × (x2) × (2) × (-x)
According to the identity, x3 + y3 + z3 - 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx)
= (x2 + 2 - x)[(x2)2 + (2)2 + (-x)2 - (x2) × (2) - (2) × (-x) - (x2) × (-x))
= (x2 - x + 2)(x4 + x2 + 4 - 2x2 + 2x + x3)
= (x2 - x + 2)(x4 + x3 - x2 + 2x + 4)
Thus, the facotrs of x6 + 5x3 + 8 are (x2 - x + 2)(x4 + x3 - x2 + 2x + 4).
[By adding and subtracting x3 on both sides]
= (x2)3+ (2)3+ (-x)3 - 3 × (x2) × (2) × (-x)
According to the identity, x3 + y3 + z3 - 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx)
= (x2 + 2 - x)[(x2)2 + (2)2 + (-x)2 - (x2) × (2) - (2) × (-x) - (x2) × (-x))
= (x2 - x + 2)(x4 + x2 + 4 - 2x2 + 2x + x3)
= (x2 - x + 2)(x4 + x3 - x2 + 2x + 4)
Thus, the facotrs of x6 + 5x3 + 8 are (x2 - x + 2)(x4 + x3 - x2 + 2x + 4).
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not perfect but I hope it helps
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