The "slide and divide" method is a way to factor second degree poynomials of the form ax² + bx + c, and is designed for the "hard" case, when the a value of the second degree polynomial is not 1.

This method will be illustrated by using an example.  Suppose we want to factor 3x² + x - 10.

1)  "Slide" the a value (3) to the end by multiplying it by c (-10).  We get:  x² + x - 30.

2)  We have created the "easy" version, where a = 1.  Factor using reverse FOIL (or your favorite method).  We get:

     (x - 5)(x + 6)

3)  Now divide the number parts of these binomials by the value a (3):

     (x + 6/3)(x - 5/3)

4)  Reduce. 

     (x + 2)(x - 5/3)

5)  If we still have a fraction in either of the binomials, move the denominator from the bottom of the fraction to the coefficient of the variable:

     (x + 2)(3x - 5)

6)  Check by multiplying back to see if it matches our original polynomial:

     (x + 2)(3x - 5) = 3x² + x - 10

     We have our original polynomial, so we have found the correct factors.