Question

How do you factor by grouping `2n^2 + 3n - 9`?

Answer 1

`2n^2+3n-9`

first try extracting the sum and difference of squares:
`color(white)("XXXXX")` `= (n^2-9) + (n^2+3n)`

factor the two resulting terms:
`color(white)("XXXXX")` `(n-3)(n+3) + n(n+3)`

extract the common term:
`color(white)("XXXXX")` `(n+3)* ((n-3)+(n))`

simplify
`color(white)("XXXXX")` `(n+3)(2n-3)`