Question

How do you write `x^2-13x+12` in factored form?

Answer 1

`x^2-13x+12=color(red)((x-1)(x-12))`

Explanation:

Remember
`color(white)("XXX")(x+color(blue)a) * (x+color(lime)b))=x^2+(color(blue)a+color(lime)b)x+color(blue)acolor(lime)b`

So we are looking for two values, `color(blue)a` and `color(lime)b`, such that
`color(white)("XXX")color(blue)a+color(lime)b=-13`
and
`color(white)("XXX")color(blue)a * color(lime)b = 12`