Question

PLEASE HELP

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

Answer 1

Hello from MrBillDoesMath!

Answer:

(x^4-2) (x^4 -1)

Discussion:

Let u = x^4, then

x^8 - 3x^4 + 2

= u^2 - 3u + 2

= (u -2) ( u -1)

= (x^4-2) (x^4 -1)

Thank you,

MrB

Answer 2

Answer: (x - 1)(x + 1)(x² + 1)(x⁴ - 2)

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)