Question

How do you factor `40-22x+x^2`?

Answer 1

`(x-20)(x-2)`

Explanation:

It does not matter whether the `x^2` term is at the beginning or end, as long as the `x` term is in the middle.

You might find it easier if the expression is changed to
`x^2color(red)( -)22xcolor(blue)(+)40" "larr` note the colours

Find two factors of `40` which `color(blue)("ADD")` to `22" "` ( the x term)
These are `20xx2 = 40 and 20+2 = 22`

The signs in the brackets will be `color(blue)("THE SAME")`

They will both be `color(red)("NEGATIVE")`

`(x-20)(x-2)`

Multiply out to check:

`x^2 color(red)(-2x -20x) color(blue)(+) 40`

`=x^2color(red)( -22)xcolor(blue)(+)40`