Question

Factor the polynomial x^8-6561

Answer 1

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)