Any time you have want to factor an expression in the form (a - b), you can always break it into
(sqrt(a) + sqrt(b)) (sqrt(a) - sqrt(b))
In this case, "a" would be 100x^2 and "b" would be 1.
So it can be factored to (10x + 1) (10x - 1)
When the boat is traveling upstream, it's speed is v - 3, and similarly for downstream its v + 3, where v is the speed of the boat relative to the water.
The time to go upstream is 3/(v-3) and to go downstream its 3/(v+3). With total time = 8, we have
3/(v-3) + 3/(v+3) = 8.
The rational zeros theorem is a method to determine the possible roots of a function. The rational zeros are p/q, where p are all of the factors of the constant term, and q are all of the factors of the leading coefficient.
For this function, p = +/- 28, +/- 14, +/- 7, +/- 4, +/- 2, +/-1.