Slide and Divide Method

• Start by sliding the number in front of the x^2 to the back number by multiplying
• Factor the trinomial like normal, looking for two numbers that multiply to give you the last term and add to give you the middle term
• After you have factored the trinomial, divide both numbers by the number you slid at the beginning
• Reduce all fractions to their simplest form
• If you still have fractions left, move the denominator in front of the x to get rid of the fraction
  

• Slide the 3 to the -8 to get x^2 + 2x - 24
• Find two numbers that multiply to give you -24 and add to give you 2 (these numbers are 6 AND -4)
• Use these two numbers to factor. You get (x + 6)(x - 4)
• Divide both numbers by 3 (the number you slid at the beginning): (x + 6/3)(x - 4/3)
• Simplify anything you can: (x + 2)(x - 4/3)
• Since we still have a fraction in the second factor, move the 3 in front of the x to get rid of it. This will give you (x + 2)(3x - 4)
  

The only difference when solving is once you have your trinomial factored, set each factor equal to zero so you can get x by itself.

• Factor like we did in the last example.
  
• Slide the 8 to get x^2 - 10x - 24 = 0
• Find two numbers that multiply to give you -24 and add to give you -10 (these numbers are -12 and 2)
• Factor using the two numbers: (x - 12)(x + 2) = 0
• Divide each number by the 8 you slide at the beginning: (x - 12/8)(x + 2/8) = 0
• Simplify your fractions: (x - 3/2)(x + 1/4) = 0
• Get rid of the fractions by moving the denominator in front of x: (2x - 3)(4x + 1) = 0
• To solve, set each factor equal to 0 and get x by itself

2x = 3, 4x = -1

x = 3/2, x = -1/4