Factor the polynomial x^8-6561

Step-by-step explanation:

x⁸ - 6561 = x⁸ - 3⁸ = (x⁴) ² - (3⁴) ²

= (x⁴ + 3⁴) (x⁴ - 3⁴) {a² - b² = (a+b) (a-b); here a = x⁴ and b = 3⁴ }

= (x⁴ + 3⁴) ([x²]² - [3²]²) {here a = x² and b = 3²}

= (x⁴ + 3⁴) (x² + 3²) (x² - 3²)

= (x⁴ + 81) (x² + 9) (x + 3) (x-3)