Question

What is the missing number that will complete the factorization? a2 + 8a + 12 = (a + 2)(a + )

Answer 1

Answer:

The missing number that will complete the factorization is 6 .

Step-by-step explanation:

 Given : Polynomial $a^2+8a+12$

We have to factorize the given  Polynomial $a^2+8a+12$ and complete the given factorization.

Consider the given  Polynomial $a^2+8a+12$

Simplifying using middle term splitting method,

Writing 8a as the sum of two terms such that the product of  these term is the product of remaining two terms.

8a can be written as  2a + 6a

We get,

$a^2+8a+12$ as $a^2+2a+6a+12$

Taking a common from first two term and 6 common from last two terms, we have,

$a^2+2a+6a+12=a(a+2)+6(a+2)$

Simplifying, we get,

$a(a+2)+6(a+2)=(a+6)(a+2)$

Thus, the missing number that will complete the factorization is 6 .

Answer 2

It is 6. I found this by diving 12 by 2 because 2 and the missing number need to have a product of 12. Here's the proof if you want it!

(a+2)(a+6)

a^2 + 2a + 6a + 12

a^2 + 8a + 12