If x + 2 is a factor of x^2 +mx + 14 find m

Hey there!

We can do this by drawing a rectangle like the one in the image. Please pardon my handwriting.

To find the side that is labeled "m - 2", we have to find what can be multiplied by 2 to get 14, which is in the bottom right square.
14 / 2 = 7  

This means that 7 = m - 2. Add 2 to each side and you get 9 = m.  

Let's check that this works with the rest of the equation. This is labeled "CHECK" in the image. 

The four terms we now have from this are: 
x², 2x, 7x, and 14. 
Combine like terms to get:
x² + 9x + 14 

This means that the value of m is 9.

Hope this helps!