Question

How do you factor `5x^2-13x+6`?

Answer 1

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

Explanation:

`5x^2 -13x +6`

Find factors of `5 and 6` which ADD (because of the PLUS 6) to give 13. Try different combinations of products:

`color(white)(xxxx)5" "6`

`color(white)(xxxx)5" "3" "rarr1xx3 = 3" "larr` cross multiply
`color(white)(xxxx)1" "2" "rarr5xx2 = ul10" "larr` cross multiply
`color(white)(xxxxxxxxxxxxxxxxxxx)13" "larr` right combination

This means we have the correct combination of the factors.
The top row gives us one bracket and the bottom row the other:

Now for the signs in the brackets..

The PLUS (+6) indicates that the signs in the brackets are the SAME
They are both NEGATIVE ( because of -13)

`5x^2 -13x +6`

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

You can always check the factors by multiplying out the brackets. (FOIL).