Question

How do you factor completely `x^4 - 3x^2 - 10`?

Answer 1

`(x^2 + 2)(x + sqrt5)(x - sqrt5)`

Explanation:

`y = x^4 - 3x^2 - 10`.
Call x^2 = X. Factor the quadratic trinomial:
`x^2 - 3x - 10.`
Find 2 numbers knowing sum (b = -3) and product (c = -10). They are the factor pair: (2, -5).
`y = (X + 2)(X - 5) = (x^2 + 2)(x^2 - 5) = (x^2 + 2)(x - sqrt5)(x + sqrt5)`