Question

Factorise x to the power of 4n + x to the power of 2n + 1 completely where n is an odd integer.​

Answer 1

• 
  `x^(3)x^(4m)(x^(4m+1) + 1)`

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• x⁴ⁿ + x²ⁿ⁺¹ = x²ⁿ⁺¹(x²ⁿ⁻¹ + 1)

n is an odd integer, let n = 2m + 1

Then

• 2n - 1 = 2(2m + 1) - 1 = 4m + 2 - 1 = 4m + 1
• 2n + 1 = 2(2m + 1) + 1 = 4m + 2 + 1 = 4m + 3
• x²ⁿ⁺¹(x²ⁿ⁻¹ + 1) =
• 
  `x^(4m + 3)(x^(4m+1) + 1)` =
• 
  `x^(3)x^(4m)(x^(4m+1) + 1)`