How do you factor the expression 4x^4-6x^2+2?

1 Answer
George C.
May 12, 2018

4x^4-6x^2+2 = (x-1)(x+1)(2x-sqrt(2))(2x+sqrt(2))

color(white)(4x^4-6x^2+2) = 4(x-1)(x+1)(x-sqrt(2)/2)(x+sqrt(2)/2)

Explanation:

Given:

4x^4-6x^2+2

Note that the sum of the coefficients is zero, i.e. 4-6+2=0.

So we can tell that x=+-1 are zeros and (x-1)(x+1) = x^2-1 is a factor.

Also all of the terms are divisible by 2, so we could separate that out as a factor, but given what we find, it's probably better to leave it in there until the end:

4x^4-6x^2+2 = (x^2-1)(4x^2-2)

color(white)(4x^4-6x^2+2) = (x^2-1^2)((2x)^2-(sqrt(2))^2)

color(white)(4x^4-6x^2+2) = (x-1)(x+1)(2x-sqrt(2))(2x+sqrt(2))

color(white)(4x^4-6x^2+2) = 4(x-1)(x+1)(x-sqrt(2)/2)(x+sqrt(2)/2)

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