Question

How do you factor `x^2 + 8x + 12`?

Answer 1

`x^2+8x+12=color(green)((x+2)(x+6))`

Explanation:

In general
`color(white)("XXX")(x^2+(color(red)(a)+color(blue)(b))x+color(red)(a)*color(blue)(b))=(x+color(red)(a))(x+color(blue)(b))`

`8 = color(red)(2)+color(blue)(6)`
and
`12=color(red)(2)*color(blue)(6)`

So
`x^2+8x+12`

`color(white)("XXX")=(x^2+(color(red)(2)+color(blue)(6))x+color(red)(2)*color(blue)(6)`

`color(white)("XXX")=(x+color(red)(2))(x+color(blue)(6))`