Same Math › Algebra 1 · grades 8–10 › Slide and divide
What is slide and divide?
Slide and divide is a shortcut for factoring when there's a number in front of x², like 2x² + 7x + 3. Slide the 2 onto the 3 to get x² + 7x + 6, which is easy: (x + 1)(x + 6). Then divide each number by 2, reduce, and move any leftover denominator up in front of the x: (2x + 1)(x + 3).
- Slide: multiply a onto c, so the x² stands alone.
- Divide: divide each number in the factors by the a you slid.
- Bottoms up: a denominator left after reducing moves in front of x.
Why schools teach it
It turns the hard case into the easy case
Factoring ax² + bx + c when a isn't 1 is the hardest factoring in Algebra 1 (HSA.SSE.B.3a). Trial and error with (2x + ?)(x + ?) can take many guesses.
Sliding a onto c makes a problem kids already know how to do. Dividing back by a undoes the slide. It's the same math as the AC method and grouping, packed into steps that are easy to remember.
At the kitchen table
What to say, and what to skip
Say this
What do you get when you slide a onto c?
Multiply them.Can you factor the new one like normal?
Now divide each number by a. Does it reduce?
If a denominator is left, where does it go?
Up in front of the x.
Skip this
- Forgetting to divide back.(x + 1)(x + 6) is the answer to a different problem.
- Not reducing before moving the bottom up.6/2 reduces to 3, so that factor is just (x + 3).
- Using it when there's a GCF.Pull out the GCF first: 4x² + 14x + 6 starts as 2(2x² + 7x + 3).
See it in action
Factoring 3x² − 5x − 2
Slide the 3 onto −2
x² − 5x − 6Factor it
(x − 6)(x + 1)Divide each number by 3 and reduce
(x − 6/3)(x + 1/3) → (x − 2)(x + 1/3)Move the 3 up in front of the x
(x − 2)(3x + 1)
Check by multiplying: 3x² + x − 6x − 2 = 3x² − 5x − 2.
Free practice sheet
Make a slide and divide sheet
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Parents also ask
Why does it work?
Sliding multiplies the whole problem by a in a hidden way; dividing by a at the end undoes it. Teachers show the full reason with grouping.
Do teachers accept it?
Most Algebra 1 teachers who teach it accept it fully. Some prefer grouping or the box because they show every step. Use your child's class method.
What if the fraction doesn't reduce?
Then the whole denominator moves up: x + 1/2 becomes 2x + 1.
Is this the same as the AC method?
It finds the same two numbers (the ones that multiply to a × c). The AC method then splits the middle term and groups.