4x^6+4x-12
4(x^6+x-3)
Now I haven't memorized any way to factor sixth-order equations...but we can use Newton's genius :)
x-(f(x)/(dy/dx))
x-(x^6+x-3)/(6x^5+1)
(5x^6+3)/(6x^5+1), if we let x1=1 we get:
1, 8/7, 1.11, 1.1117, 1.1117564746368137533445820441994, and my calculator keeps repeating there as that is the end of its precision so if you'd like to go further.
You would divide (x^6+x-3) by (x-1.1117...) to get the next factor :)