Factoring: Find the Rectangle

Lesson 8 of 12 · 7 min · Free, no account needed

What you will learn

To factor x² + bx + c, fold its tiles into a rectangle: its sides are the factors (x + p)(x + q).
The strips split into p and q, so p + q = b. The corner holds p × q = c units.
Not every pile folds: x² + 3x + 5 has no whole-number split, so it makes no rectangle.

This frame is (x + 2) by (x + 3). Which pile fills it exactly?
Tap a pile to pour it in.
One big square, five strips, six little tiles. Make a perfect rectangle.
Drag each strip to the right of the square or below it. The 6 units pour into the corner the strips make.
Fold x² + 8x + 15.
Turn p and q. Both counts must match the pile.
Folding a pile is factoring.
Factoring runs expanding backwards: from x² + 5x + 6 back to the sides (x + 2)(x + 3).
The strips split into two groups, so p + q = 5. The corner is p by q, so p × q = 6.
So to factor x² + bx + c, look for two numbers that add to b and multiply to c.
Which piles fold into a rectangle?
Tap a pile, then its bin. Look for two numbers that add to the strips and multiply to the units.
Game: rectangle rush.
Fold four piles before the 60 seconds run out.
A loop can try every split for you.
This program tries each way to split 5 strips. Press Run.
Make a pile of your own that folds.
Choose how many strips and units go with the x². Check folds it.
Spot the impostor.
Your pile is in the line-up. One pile can never be a rectangle. Tap piles to fold them, then pick the impostor.

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