Question

How do you factor `4y^2-11y-3`?

Answer 1

`4y^2-11y-3 = (4y+1)(y-3)`

Explanation:

Since `(ay+b)(cy+d) = acy^2+ (ad+bc)y + bd`

We are looking for
`color(white)("XXXX")`factors `a` and `c` of 4
`color(white)("XXXX")`and
`color(white)("XXXX")`factors `b` and `d` of `(-3)`
such that
`color(white)("XXXX")` `ad + bc = -11`

Factors of 4: `{ (1,4), (2,2) }`
Factors of (-3): `{ (1,-3), (-1,3) }`

With only a few possible factor combinations the solution can be found rather quickly.,