Question

How do you factor `x^2-8x-48`?

Answer 1

`x^2-8x-48=(x+4)(x-12)`

Explanation:

To factorize a polynomial of general form `ax^2+bx+c`, one should divide middle term `bx` in two parts, whose sum is `b` and product is `axxc`.

So for `x^2-8x-48`, we should divide `-8x` in two parts which add up to `-8` and whose product is `1xx(-48)=-48`.

A few trial indicate them to be `-12` and `4`. Hence

`x^2-8x-48=x^2-12x+4x-48` or

`x(x-12)+4(x-12)` or

`(x+4)(x-12)`