Question

How do you factor the expression `3x^2 + 12x + 12=0`?

Answer 1

`3x^2+12x+12=0 hArr color(green)(3(x+2)^2=0`

Explanation:

`3x^2+12x+12`
`color(white)("XXX")=3(x^2+4x+4)`
`color(white)("XXX")=3(x+2)^2`

Answer 2

`x=-2`

Explanation:

To factor the expression in general form `ax^2+bx+c=0`, one has to identify factors of `a*c`, whose sum is `b`.

In `3x^2+12x+12=0`, `a*c=36` and `b=12`, so factors of `36` whose sum is `12` are `6` and `6`. Hence `3x^2+12x+12=0` can be expressed as

`3x^2+6x+6x+12=0` i.e.

`3x(x+2)+6(x+2))=0` or

`(3x+6)(x+2)=0` i.e.

either `(3x+6)=0` or `(x+2)=0`

i.e. `x=(-6)/3=-2 or -2` and as they are same we have a unique solution `x=-2`