Question

How do you factor by grouping with three terms `252v + 48v ^2 -12v ^3`?

Answer 1

First simplify by extracting the obvious factor of `12v`
`252v+ 48v^2-12v^3`
`=12v(21+4v-v^2)`
or
`=(-12v)(v^2-4v-21)`

`21` can be factored as `3xx7`
and the difference between 3 and 7 is 4

so
`= (-12v)(v^2+3v-7v-21)`

`=(-12v)(v(v+3) - 7(v+3))`

`=(-12v)(v-7)(v+3)`