The factors of x8 + x4 + 1 are :(a) (x4 + 1 – x2) (x2 + 1 + x) (x2 +

1.	The factors of x8 + x4 + 1 are :(a) (x4 + 1 – x2) (x2 + 1 + x) (x2 + 1 – x) (b) (x4 + 1 – x2) (x2 - 1 + x) (x2 + 1 + x)(c) (x4 - 1 + x2) (x2 - 1 + x) (x2 + 1 + x)(d) (x4 - 1 + x2) (x2 + 1 - x) (x2 + 1 + x)
Answer» (a) (x⁴ + 1 – x²) (x² + 1 + x) (x² + 1 – x) x⁸ + x⁴ + 1 = x⁸ + 2x⁴ + 1 – x⁴ (Adding and subtracting x⁴) = (x⁴ + 1)² – (x²)² = (x⁴ + 1 + x²) (x⁴ + 1 – x²) = [(x⁴ + 2x² + 1) – x²] (x⁴ + 1 – x²) = [(x² + 1)² – (x)²] (x⁴ + 1 – x²) = (x² + 1 + x) (x² + 1 – x) (x⁴ + 1 – x²)

The factors of x8 + x4 + 1 are :(a) (x4 + 1 – x2) (x2 + 1 + x) (x2 + 1 – x) (b) (x4 + 1 – x2) (x2 - 1 + x) (x2 + 1 + x)(c) (x4 - 1 + x2) (x2 - 1 + x) (x2 + 1 + x)(d) (x4 - 1 + x2) (x2 + 1 - x) (x2 + 1 + x)

Answer»

(a) (x⁴ + 1 – x²) (x² + 1 + x) (x² + 1 – x)

x⁸ + x⁴ + 1 = x⁸ + 2x⁴ + 1 – x⁴ (Adding and subtracting x⁴)

= (x⁴ + 1)² – (x²)² = (x⁴ + 1 + x²) (x⁴ + 1 – x²)

= [(x⁴ + 2x² + 1) – x²] (x⁴ + 1 – x²)

= [(x² + 1)² – (x)²] (x⁴ + 1 – x²)

= (x² + 1 + x) (x² + 1 – x) (x⁴ + 1 – x²)