Question

How do you factor `p^4+5p^2+6`?

Answer 1

(p^2 + 2)(p^2 + 3)

Explanation:

Call `x = p^2`, the trinomial transforms to:
`f(x) = x^2 + 5x + 6.` Factor f(x).
Find 2 numbers knowing sum (5) and product (6). They are 2 and 3.
`f(x) = (x + 2)(x + 3)`
`f(p) = (p^2 + 2)(p^2 + 3)`

If being asked, you can continue factoring with complex numbers.
`f(p) = (p - isqrt2)(p + isqrt2)(x - isqrt3)(x + isqrt3)`