Question

How do you simplify `4x^2+3x+1-8x`?

Answer 1

`4x^2+3x+1-8x`

`=4x^2+3x-8x+1`

`=4x^2+(3-8)x+1`

`=4x^2-5x+1`

`=(4x-1)(x-1)`

Incidentally, there are a few different ways to spot this last step, including this little trick:

Given `4x^2-5x+1`, extract the digits to get `451` and factor that to get `41xx11`. Then taking the `-` sign into account, `41` becomes `(4x-1)` and `11` becomes `(x-1)`. (This only works if the multiplication involves no carrying of digits)