Factor the expression completely.x, to the power 4 , plus, 2, x, squared, minus, 24x 4 +2x 2 −24

Sure, let's factor the expression step by step:

1. First, write down the expression: x^4 + 2x^2 - 24

2. Notice that this is a quadratic equation in the form of ax^2 + bx + c, where x^2 is replaced by y (let y = x^2). So, rewrite the equation as: y^2 + 2y - 24

3. Now, factor the quadratic equation. We are looking for two numbers that multiply to -24 and add to 2. The numbers 6 and -4 satisfy these conditions. So, we can write the equation as: (y - 4)(y + 6)

4. Substitute y = x^2 back into the equation to get: (x^2 - 4)(x^2 + 6)

5. The term (x^2 - 4) can be factored further as it is a difference of squares. It factors to (x - 2)(x + 2).

6. So, the completely factored expression is: (x - 2)(x + 2)(x^2 + 6)