Answer:
[tex](x+2)(x-2)(x+1)(x-1)[/tex]
Step-by-step explanation:
STEP 1: Rewrite [tex]x^{4}[/tex] as [tex](x^2)^2[/tex].
[tex](x^2)^2-5x^2+4[/tex]
STEP 2: Let [tex]u=x^{2}[/tex]. Substitute [tex]u[/tex] for all occurrences of [tex]x^{2}[/tex].
[tex]u^2-5u+4[/tex]
STEP 3: Factor [tex]u^2-5u+4[/tex] using the AC method.
[tex](u-4)(u-1)[/tex]
STEP 4: Replace all occurrences of [tex]u[/tex] with [tex]x^2[/tex].
[tex](x^{2} -4)(x^{2} -1)[/tex]
STEP 5: Rewrite [tex]4[/tex] as [tex]2^{2}[/tex].
[tex](x^{2}-2^{2})(x^{2}-1)[/tex]
STEP 6: Since both terms are perfect squares, factor using the difference of squares formula,[tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=x[/tex] and [tex]b=2[/tex].
[tex](x+2)(x-2)(x^{2}-1)[/tex]
STEP 7: Rewrite [tex]1[/tex] as [tex]1^{2}[/tex].
[tex](x+2)(x-2)(x^2-1^2)[/tex]
STEP 8: Factor.
[tex](x+2)(x-2)(x+1)(x-1)[/tex]
