How Do I Factor 2x^3-5x^2-2x+5?

First, note that the coefficients are 2, 5, 2, 5, suggesting that if you factor x² out of the first two terms, you might have something that looks like the last two terms.
2x³-5x²-2x+5
 = x²(2x-5) - 2x + 5
 = x²(2x-5) - (2x-5)
 = (x²-1)(2x-5)
Now, you use the "formula" for factoring (x²-1):
 = (x-1)(x+1)(2x-5)

(a²-b²) = (a-b)(a+b) is a good formula to memorize for algebra.