Solve x^8-3x^4+2 by rewriting the equation using the substitution of u as a quadratic equation. (show work)

 (x - 1)(x + 1)(x² + 1)(x⁴ - 2)

Step-by-step explanation:

Given: x⁸ - 3x⁴ + 2

Let u = x⁴

then we get: u² - 3u + 2

Factor: (u - 1)(u - 2)

Substitute (replace u): (x⁴ - 1)(x⁴ - 2)    repeat these steps for x⁴ - 1  

x⁴ - 1

Let u = x²

then we get: u² - 1

Factor: (u - 1)(u + 1)

Substitute (replace u): (x² - 1)(x² + 1)         factor x² - 1

x² - 1

Factor: (x - 1)(x + 1)

Next, put all the factors together.  You should have 8 x's (degree of 8)

(x⁴ - 2)(x² + 1) (x - 1)(x + 1)

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step-by-step explanation:

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