Question

How do you factor `5a^2 - 5a - 100`?

Answer 1

Extract the obvious numeric factor of `5` from `5a^2-5a-100` to get
`color(white)("XXXX")` `5(a^2-1a-20)`

So we are looking for two numbers, `p` and `q`
such that
`color(white)("XXXX")` `p+q = -1`
and
`color(white)("XXXX")` `p*q = -20`

With only a little consideration of the options, we get
`color(white)("XXXX")` `(4,-5)`
and the final factors are
`color(white)("XXXX")` `=5(a+4)(a-5)`