Question

How do you solve `3x^2-13x-10=0` by factoring?

Answer 1

`(3x+2)(x-5)`

Explanation:

Because `3` can only have factors of `3` and1
you know those will be your coefficients for `x`.
That is your factors will be of the form
`color(white)("XXX") (3x +a)(x +b )`

You also know that one of `a` or `b` will have `+` and one side will have `-` due to the `color(red)(-)10`.

The options for `10` are
`2xx5` or `1x10`.

Using `2xx5`
if you multiply the `5` by `3` it gives you `15`
and the `2` by `1`1 you get `2`.

Because `13` in the center (of the original form) is negative
you know the `5` needs to be negative

and the factors are
`color(white)("XXX")(3x+2)(x-5)`