Question

How do you factor `9 - 6a - 24a^2`?

Answer 1

Given `9-6a-24a^2`

Extract the common constant factor of 3
`=3(3-2a-8a^2)`

Examine factors of 3 and -8
Remembering `(p+qa)(r+sa) = pq + (ps+qr)a +(qs)a^2`
where in this case `pq = 3`, `ps+qr = -2`, and `qs= -8`

Note that `3xx1 = 3`
and `4xx(-2) = -8`
and `3xx(-2)+(4)xx1 = -2`

So we can continue to factor:
`=3(3+4a)(1-2a)`