The factors of 4 x3+12 x2+6x+18 are:
4x2+6
3x3+2
The expression 4 x3+12 x2+6x+18 can be written as
(4 x3+12 x2)+(6x+18)
Taking the common factor 4 x2 from the first two terms and 6 from the last two terms, we get
=4 x2(x+3)+6(x+3)
Taking (x+3) common, we get
=(x+3)(4 x2+6)
Therefore,4 x3+12 x2+6x+18=(x+3)(4 x2+6)
Thus, (x+3) and (4 x2+6) are the two factors.