Question

Factor the expression completely. 10x^2−x^4−21

Answer 1

− (x^2 − 7) (x^2 − 3)

Explanation:

1. Factor −1 out of 10x^2 − x^4 − 21. You now have − (x^4 − 10x^2 + 21).

2. Rewrite x^4 as (x^2)^2. You now have − ((x^2)^2 − 10x^2 + 21).

3. Let u = x^2. Substitute u for all occurrences of x^2. You now have − (u^2 − 10u + 21).

4. Factor u^2 − 10u + 21 using the AC method. You now have - ((u - 7) (u - 3))

5. Factor. − (x^2 − 7) (x^2 − 3).