Math

How do you factor "0 = x^4 - 6x^2 + 5"? Please show all steps.

Here's my work, but I just went around in circles.....

0 = x^4 - 6x^2 + 5
-5 = x^4 - 6x^2
-5 = x^2 (x^2 - 6)
-5 / x^2 = x^2 - 6
(-5 / x^2) + 6 = x^2
(-5 + 6x^2) / (x^2) = x^2
-5 + 6x^2 = x^2 * x^2
-5 + 6x^2 = x^4
0 - x^4 - 6x^2 + 5

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  1. NO, you have not factored anything at all

    x^4 - 6x^2 + 5 = 0
    (x^2 - 1)(x^2 - 5) = 0
    (x-1)(x+1)x^2 - 5) = 0 if you factor over the rationals

    (x-1)(x+1)x-√5)(x+√5) = 0 if you factor over the reals

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  2. start by treating the problem like it is a quadratic. Let u = x^2

    u^2 - 6u + 5

    Factors as: (u-5)(u-1)

    (x^2 -5)(x^2 -1) =0

    Whenever there is = 0, Normally, you have to solve for x and not stop at the factoring step.

    Set each factor = to zero.
    (x^2-5)=0 or (x^2 - 1) = 0
    x^2 = 5 or x^2 = 1
    x = square root of 5 divided by 2
    x = minus the square root of 5 divided by 2
    x = 1
    x = -1

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