The Slide Method of factoring can be used on Trinomials whose leading coefficient is not one.
It takes the guess work out of factoring.
Let us begin with the general form of a trinomial, Ay2 + By + C.
Our first example will be to factor 6y2 - y - 2.
| Step | Example | |
| 1. Begin with Ay2 + By + C |
6y2 - y - 2 | |
| 2. Multiply A x C and throw away A: y2 + By + AC | y2 - y - 12 | |
| 3. Factor the new problem (leading coefficient is one) | (y - 4) (y + 3) | |
| 4. Divide by the throwaway A | 
|
|
| 5. REDUCE (not necessary in equation solving) | 
|
|
| 6. Slide | (3y - 2) (2y + 1) |
Here is another example: 3x2 + x - 10.
(Always pull out any common factors before continuing with this method).
First you slide the leading coefficient to the end and multiply it by the constant:
You get x2 + x - 30
Then factor like you normally would:
(x + 6)(x - 5)
You have to undo the number you slid out. You do this by dividing the constant in each factor by the leading coefficient you "slid" out of the way.
(x + 6/3)(x - 5/3)
Simplify the fractional terms you end up with.
(x + 2)(x - 5/3)
Once it's simplified, if there's a fraction left, the denominator becomes the coefficient of the variable term.
ANSWER: (x + 2)(3x - 5)
Here's another example without the explanations:
2x2 - 7x + 5
x2 - 7x + 10
(x - 5)(x - 2)
(x - 5/2)(x - 2/2)
(x - 5/2)(x - 1)
ANSWER: (2x - 5)(x - 1)
Finally, an example where you have to pull out a common factor first:
12x10 + 42x9 + 18x8
6x8(2x2 + 7x + 3)
6x8(x2 + 7x + 6)
6x8(x + 6)(x + 1)
6x8(x + 6/2)(x + 1/2)
6x8(x + 3)(x + 1/2)
6x8(x + 3)(2x + 1)