Question

How do you factor the trinomial `7u^2+26u-8`?

Answer 1

`(7u-2)(u+4)`

Explanation:

`color(red)(7)u^2+color(blue)26ucolor(red)(-8)`

For expansion, first
multiply `color(red)7` with `color(red)(-8)`, which is `=-56`, then

Find 2 numbers whose product is `-56` and sum is `color(blue)26`, that is `color(green)28` and `color(green)(-2)`.

Factorization by expansion :
`7u^2+color(green)(28u-2u)-8`

Now, take common on first 2 terms and last 2 terms seperately,
`7u(u+4)-2(u+4)`

Further, taking common on `(u+4)`:
`(7u-2)(u+4)`