Simplifying
x4 + 7x3 + 12x2

Reorder the terms:
12x2 + 7x3 + x4

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(12 + 7x + x2)

Factor a trinomial.
x2((4 + x)(3 + x))

Final result:
x2(4 + x)(3 + x)