Question

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

Answer 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

Answer 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