Answer:
The missing number that will complete the factorization is 6 .
Step-by-step explanation:
Given : Polynomial [tex]a^2+8a+12[/tex]
We have to factorize the given Polynomial [tex]a^2+8a+12[/tex] and complete the given factorization.
Consider the given Polynomial [tex]a^2+8a+12[/tex]
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,
[tex]a^2+8a+12[/tex] as [tex]a^2+2a+6a+12[/tex]
Taking a common from first two term and 6 common from last two terms, we have,
[tex]a^2+2a+6a+12=a(a+2)+6(a+2)[/tex]
Simplifying, we get,
[tex]a(a+2)+6(a+2)=(a+6)(a+2)[/tex]
Thus, the missing number that will complete the factorization is 6 .
