Math
posted by Anonymous on .
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

NO, you have not factored anything at all
x^4  6x^2 + 5 = 0
(x^2  1)(x^2  5) = 0
(x1)(x+1)x^2  5) = 0 if you factor over the rationals
(x1)(x+1)x√5)(x+√5) = 0 if you factor over the reals 
start by treating the problem like it is a quadratic. Let u = x^2
u^2  6u + 5
Factors as: (u5)(u1)
(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^25)=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