1)) Factor \( x^{4}-8 x^{2}-9 \) completely. All factors in your answer should have integer coefficients.

To factor the polynomial \( x^{4}-8 x^{2}-9 \), we can start by making a substitution. Let \( y = x^2 \). The expression becomes \( y^2 - 8y - 9 \). Now we need to factor this quadratic polynomial. First, we can rewrite it as \( (y - 9)(y + 1) \). Next, substituting back \( y = x^2 \) gives us: \[ (x^2 - 9)(x^2 + 1) \] Now we can factor \( x^2 - 9 \) further since it is a difference of squares: \[ (x - 3)(x + 3)(x^2 + 1) \] Putting it all together, the completely factored form of \( x^{4}-8 x^{2}-9 \) is: \[ (x - 3)(x + 3)(x^2 + 1) \]