Step by Step
1
Slide — multiply a and c
Multiply the leading coefficient (a) and the constant (c) together.
2
Factor using that product
Find two numbers that multiply to give you the a×c product and add to give you b, just like factoring a simple trinomial.
3
Divide — divide by a
Divide those two numbers by the original leading coefficient a.
4
Simplify
Reduce any resulting fractions, and if a whole number is left in a denominator, move it in front of the variable as a coefficient instead.
Applied Walkthrough
1
Factor 2x² + 7x + 3, where a = 2, b = 7, c = 3. Slide: multiply a × c = 2 × 3 = 6.
2
Find two numbers that multiply to 6 and add to 7: those numbers are 6 and 1.
3
Divide: 6/2 = 3 and 1/2. Since 1/2 has a in the denominator still, move the 2 in front of x instead, giving (x + 3)(2x + 1).
4
Check by FOILing (x + 3)(2x + 1): 2x² + x + 6x + 3 = 2x² + 7x + 3 — matches the original.
Exam Application
Exams test whether you can execute all four slide-and-divide steps correctly, especially the final simplification step where a leftover fraction needs to become a coefficient rather than being left as a fraction.
⚠ Common Trap
The most common trap is forgetting the final simplification step — leaving a fraction in one of the factors instead of moving the denominator to become the variable's coefficient.
✓ Quick Self-Check
1. What is the first step of Slide and Divide?
Multiply the leading coefficient (a) and the constant (c) together.
Tap to reveal / hide
2. Factor 2x² + 7x + 3 using slide and divide.
(x + 3)(2x + 1).
Tap to reveal / hide
3. When is slide and divide needed instead of simple factoring?
When the leading coefficient a is not equal to 1.
Tap to reveal / hide
4. What do you do if dividing leaves a fraction like 1/2 in a factor?
Move the denominator to become the coefficient of the variable instead of leaving a fraction.
Tap to reveal / hide
5. How can you verify a slide-and-divide factoring result?
FOIL the factored answer back out and confirm it matches the original trinomial.
Tap to reveal / hide