factor ( x^4 - 10x^2 + 9 ) completely. all factors in your answer should have integer coefficients.

Answer:

$(x - 1)(x + 1)(x - 3)(x + 3)$

Explanation:

Step1: Substitute $u = x^2$

$u^2 - 10u + 9$

Step2: Factor the quadratic

$(u - 1)(u - 9)$

Step3: Replace $u$ with $x^2$

$(x^2 - 1)(x^2 - 9)$

Step4: Factor difference of squares

$(x - 1)(x + 1)(x - 3)(x + 3)$