Question

How do you factor `8u^2 + 6u - 9`?

Answer 1

`8u^2+6u-9 = (2u+3)(4u-3)`

Explanation:

We need to look at factors of
`color(white)("XXXX")` `8`
`color(white)("XXXX")` `(a,b) epsilon {(1,8), (2,4)}`
and
`color(white)("XXXX")` `(-9)`
`color(white)("XXXX")` `(c,d) epsilon {(1,-9), (-1,9), (3,-3), (-3,3)}`

such that
`color(white)("XXXX")` `ac - bd = +6`

then plug them into
`color(white)("XXXX")` `(au+c)(bu+d)`