What is the factored form of 9X^2+12X+4

This is of the form ax^2+bx+c. To factor a quadratic like this you want to find two values, j and k, that satisfy two conditions.

jk=ac and j+k=b ... in this case:

jk=ac=36 and j+k=b=12, so j and k must be 6 and 6

Now you replace bx with jx and kx in the original equation which gives you:

9x^2+6x+6x+4 now factor the first and second pair of terms ...

3x (3x+2) + 2 (3x+2) which is equal to:

(3x+2) (3x+2) which is just:

(3x+2) ^2

(3X+2) ^2 or (3X+2) x (3X+2)