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

Mar 30, 2016

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

#### Explanation:

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

If being asked, you can continue factoring with complex numbers.
$f \left(p\right) = \left(p - i \sqrt{2}\right) \left(p + i \sqrt{2}\right) \left(x - i \sqrt{3}\right) \left(x + i \sqrt{3}\right)$