The diagram represents the factorization of a2 + 8a + 12. What is the missing number that will complete the factorization? a2 + 8a + 12 = (a + 2) (a + )

To factor a quadratic of the form ax^2+bx+c you need to find two values, j and k, which satisfy two conditions ...

jk=ac=12 and j+k=b=8, so j and k must be 2 and 6

Then the factors are just (a+j) (a+k), in this case:

(a+2) (a+6)

So the missing term was 6

I'm assuming the a is squared.

You have to find what multiplies to make 12 (1st number and last multiplied together) and adds to make 8 (the middle number). In this case the two numbers you need are 2 and 6, and so your missing number is 6. If you want to check, you can multiply out the brackets. Hope I explained well enough.