Multiply the two that you found to get x^2+x-6 and then divide by that.
I can't teach you polynomial division on here but you could choose a video from here..
polynomial division - YouTube.
Yes that's correct. Now factorise 25x^2-4. It's a difference of two squares.
You could also look at this page
(25x^4+25x^3-154x^2-4x+24)/(x^2+x-6) - Wolfram|Alpha