Factor the expression completely.x, to the power 4 , minus, 9, x, squared, plus, 8x 4 −9x 2 +8

The expression you provided is x^4 - 9x^2 + 8. To factor this completely, we can treat it as a quadratic equation, where x^2 is the variable.

Step 1: Rewrite the expression The expression becomes (x^2)^2 - 9(x^2) + 8.

Step 2: Factor the quadratic equation We look for two numbers that multiply to 8 and add to -9. The numbers -1 and -8 satisfy these conditions. So, we can factor the equation as follows: (x^2 - 1)(x^2 - 8)

Step 3: Factor further Both x^2 - 1 and x^2 - 8 are differences of squares and can be factored further.

x^2 - 1 can be factored into (x - 1)(x + 1). x^2 - 8 can be factored into (x - sqrt(8))(x + sqrt(8)).

So, the completely factored form of the expression x^4 - 9x^2 + 8 is (x - 1)(x + 1)(x - sqrt(8))(x + sqrt(8)).