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