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

Question

2202 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-17T11:43:44

$(x-20)(x-2)$

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:

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

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

How do you factor 40-22x+x^240-22x+x^2?