Question 368992
First you factor out the number that all three have in common which in this case is 3. SO we get:

3(w^2+9w+18)  

Then you need to find the two numbers that multiply together to equal 18 and add together to equal 9.  That would be 6 and 3 because 6*3=18, 6+3=9
So we get:
3(w+6)(w+3)   

This is fully factored.  To check you answer you would use the FOIL method to multiply the (w+6)(w+3). Then you would multiply the 3 back into that answer.

Hope this helps!


**UPDATED CHECK**

3(w+6)(w+3)  FOIL is First Outside Inside Last
3(w^2+3w+6w+18)
3(w^2+9w+18)   Then distribute the 3 through by multiplying
3w^2+27w+54