factor $x^{4}-5x^{2}+4$ completely. all factors in your answer should have integer coefficients.

Explanation:

Step1: Let (y = x^{2})

The expression becomes (y^{2}-5y + 4).

Step2: Factor (y^{2}-5y + 4)

We find two numbers that multiply to (4) and add up to (-5). The numbers are (-4) and (-1). So (y^{2}-5y + 4=(y - 4)(y - 1)).

Step3: Substitute back (y=x^{2})

We get ((x^{2}-4)(x^{2}-1)).

Step4: Factor (x^{2}-4) and (x^{2}-1) further

Using the difference - of - squares formula (a^{2}-b^{2}=(a + b)(a - b)), (x^{2}-4=(x + 2)(x - 2)) and (x^{2}-1=(x + 1)(x - 1)).

Answer:

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