The factor of [tex]$a^{2} b+2 a^{2}+3 b+6$[/tex] exists [tex]$\left(a^{2}+3\right)(b+2)$[/tex].
Let the given factor be [tex]$a^{2} b+2 a^{2}+3 b+6$[/tex]
To factor this we use the grouping method
We group the first two terms and last two terms then we factor out the greatest common factor (GCF) from each group.
[tex]$\left(a^{2} b+2 a^{2}\right)+(3 b+6)$[/tex]
Take out GCF from each group
[tex]$a^{2}(b+2)+3(b+2)$[/tex]
Now factor out b+2, we get
[tex]$\left(a^{2}+3\right)(b+2)$[/tex]
The factor of [tex]$a^{2} b+2 a^{2}+3 b+6$[/tex] exists [tex]$\left(a^{2}+3\right)(b+2)$[/tex].
To learn more about the grouping method refer to:
https://brainly.com/question/24240168
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