Question

How do you factor by grouping `25v^2+60v+27`?

Answer 1

`(5v+3)(5v+9)`

Explanation:

`color(white)(..)+color(green)(60)`
`color(white)(..)xx 675`
`* * * * * *`
`color(white)(.)1 color(white)(0)xx 675`
`color(white)(.)3 color(white)(0)xx 225`
`color(white)(.)5 color(white)(0)xx 135`
`color(white)(.)9 color(white)(0) xx 75`
`color(white)(.)15 xx 45` `=> color(red)(15)+color(red)(45) = color(green)(60)`

So we've got

`(25v^2 + color(red)(45)v) + (color(red)(15)v + 27)`

`5v(5v+9) + 3(5v+9)`

`(5v+3)(5v+9)`