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

1 Answer
Mar 30, 2016

Answer:

(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)#