How To Factor a Trinomial Using the "Slide and Divide" Method

Factoring quadratic trinomials is an essential skill in algebra.  In this blog post, I will explore factoring quadratic trinomials of the form ax² + bx + c where a ≠ 1 , using the "Slide and Divide" method.  If you are unfamiliar with this method, let me start off by telling you that it’s awesome.  This method is particularly helpful when the coefficient of x² is greater than 1.  Here's a step-by step guide in using the slide and divide method.  

Consider the trinomial 3x² + 10x + 8.

Step 1: Slide

Multiply the leading coefficient (3) by the constant term (8).  This gives you a new quadratic trinomial: x² + 10x + 24.

Step 2: Factor the New Quadratic

Next, you need to factor the new trinomial, x² + 10x + 24.  You need to find two numbers that multiply to 24 (the constant) and add to 10 (the middle coefficient).

The numbers 6 and 4 work because: (6)(4) = 24 and (6) + (4) = 10.

Now, rewrite the trinomial in factored form (x + 6) (x + 4).

Step 3:  Divide

Let's go to the "divide" part of this method.  Divide both of the numeric factors (6 and 4) by the value we slid over to step 1, which in this case is the leading coefficient 3.

This leads to:  (x + 6/3)(x + 4/3) = (x + 2)(x + 4/3)

Since we want an integer coefficients, then 4/3 is a problem! We need to slide the left over 3 up next to the variable x.

The result is (x + 2)(3x + 4).

Step 4:  Final Check

To ensure the factors are correct, you can expand (x + 2)(3x + 4) back, to check if you get the original trinomial.

Another Example:

Factor 6x² -x - 2.

1.   Slide:  Multiply (6) and (-2) to get (-12).

2.  New Quadratic:  x² -x - 12

3.  Factor:  Find two numbers that multiply to (-12) and add to (-1).  These 

     are (3) and (-4).  Let's check:  (3)(-4) = -12 and (3) + (-4) = -1.  So the 

     factors of  x² -x - 12 are (x + 3) (x - 4).

4.  Divide:  Divide both the numeric factors (3 and -4) by the number we 

     slid in step 1 which is 6, don't forget to reduce the fraction to its lowest 

     form.  Remember if the result is not an integer, we need to slide the left 

     over up next to the variable x.  

5.  Complete factors:  (2x + 1) (3x - 2)

   

    You can refer to my video below to fully grasp the trick!           

Conclusion

The slide and divide method is a systematic way to factor quadratic trinomials, especially when the leading coefficient is greater than 1. Practice with different examples to become proficient in this method!