Question

Factor x^4-5x^2+4 show your work

Answer 1

`(x+2)(x-2)(x+1)(x-1)`

Explanation:

STEP 1: Rewrite
`x^(4)` as
`(x^2)^2`.

`(x^2)^2-5x^2+4`

STEP 2: Let
`u=x^(2)`. Substitute
`u` for all occurrences of
`x^(2)`.

`u^2-5u+4`

STEP 3: Factor
`u^2-5u+4` using the AC method.

`(u-4)(u-1)`

STEP 4: Replace all occurrences of
`u` with
`x^2`.

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

STEP 5: Rewrite
`4` as
`2^(2)`.

`(x^(2)-2^(2))(x^(2)-1)`

STEP 6: Since both terms are perfect squares, factor using the difference of squares formula,
`a^2-b^2=(a+b)(a-b)` where
`a=x` and
`b=2`.

`(x+2)(x-2)(x^(2)-1)`

STEP 7: Rewrite
`1` as
`1^(2)`.

`(x+2)(x-2)(x^2-1^2)`

STEP 8: Factor.

`(x+2)(x-2)(x+1)(x-1)`