Question

How do you factor `20+6x-2x^2`?

Answer 1

`20+6x-2x^2 = (-2)(x-5)(x+2)`

Explanation:

I (personally) always find it easier to work with expressions in standard form, so I will re-write the given expression as
`color(white)("XXX")-2x^2+6x+20`

As a first step extract the obvious constant factor:
`color(white)("XXX")(-2)(x^2-3x-10)`

To factor the second part, we are looking for factors of `10` whose difference is `3`.
Again with only a bit of consideration we can come up with `(2,5)`

Since the constant term `(-10)` is negative, we know that one of `(2,5)` is negative.
Since the coefficient of `x` (i.e. `(-3)`) is also negative we know that the larger of `(2,5)` should be negative.

Therefore we can factor our expression as
`color(white)("XXX")(-2)(x-5)(x+2)`