Question

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

Answer 1

`x=-2` or `x=-6`

Explanation:

To solve `x^2+8x+12=0`, we should first factorize the polynomial `x^2+8x+12`

To factorize a quadratic polynomial of type `ax^2+bx+c`,

one needs to split middle term `b` in two parts whose product is `ac`. As in `x^2+8x+12`, the product is `1*12=12` and middle term `8`, it can be split in `6` and `2`.

Hence, `x^2+8x+12=0` can be written as

`x^2+6x+2x+12=0`

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

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

Hence, either `x+2=0` or `x+6=0` i.e.

`x=-2` or `x=-6`