Question

Is it possible to factor `3x^2+ 7x + 2`? If so, what are the factors?

Answer 1

`3x^2+7x+2" "=" " (3x+1)(x+2)`

Explanation:

The whole number factors of 3 can only be 1 and 3
The whole number factors of 2 can only be 1 and 2

`3xx2=6` which is close to 7 so lets try it!

`color(blue)("Attempt 1")`

`(3x+2)(x+1) = 3x^2+3x+2x+2 =3x^2+color(red)(5x)+2 color(red)(" Fail"`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Attempt 2")`

`(3x+1)(x+2) = 3x^2+6x+x+2 =3x^2+7x+2 color(green)(" Works!")`