How do you factor x^8 - 1/81x8−181?

1 Answer
Vikki
Dec 13, 2015

(x^8 -1/81)= (x^2 -1/3)(x^2 +1/3)(x^4 + 1/9)(x8−181)=(x2−13)(x2+13)(x4+19)

Explanation:

Given x^8 - 1/81x8−181

Using difference of square a^2 -b^2 = (a-b)(a+b)a2−b2=(a−b)(a+b)
=> (x^4)^2 -(1/9)^2⇒(x4)2−(19)2

=>(x^4 -1/9)(x^4 +1/9)⇒(x4−19)(x4+19)

Use the difference of square again...

=> (x^2 -1/3)(x^2 +1/3)(x^4 + 1/9)⇒(x2−13)(x2+13)(x4+19)

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