Question

How do you factor completely `2x^2+6x-80`?

Answer 1

y = 2(x - 5)( x + 8)

Explanation:

`y = 2(x^2 + 3x - 40)`
Factor the trinomial in parentheses.
Find 2 numbers knowing sum (b = 3) and product (c = -40).
They are (-5, 8).
y = 2(x - 5)(x + 8)

Answer 2

`2x^2+6x-80=color(blue)(2(x-5)(x+8))`

Explanation:

Given
`color(white)("XXX")2x^2+6x-80`

First observe that all the terms have a constant factor of `2`;
so we can write:
`color(white)("XXX")2(x^2+3x-40)`

Next lets think about factors of `40` whose difference is `3`

`40=2xx20` ...not a difference of `3`
`40=4xx10` ...not a difference of `3`
`40=5xx8` ...looks as if we've found it

In `(x^2+3x-40)` the last term `(-40)` is negative so one of `5` or `8` must be negative;
and the middle term `(+3x)` is positive so the larger of `5` and `8` must be positive.

Therefore our complete factors are:
`color(white)("XXX")2(x-5)(x+8)`