Factor Trinomial (Diamond) Game

Factor Trinomial (Diamond) Game
Factoring a quadratic trinomial is essentially the “reverse” of the Distributive Property. You are taking a expression that looks like x² + bx + c and breaking it back down into two binomials, like (x + m)(x + n).
 
This game, Diamond Protocol, is a digital trainer for a common algebraic technique called the Diamond Method. It helps you factor quadratic trinomials (equations that look like x² + bx + c) into two binomials. Scroll down for a detailed explanation.
 

 

How to Play the Factor Trinomial (Diamond) Game
The game is divided into two distinct phases.
Phase 1: Diamond Sync
In this phase, your goal is to find two specific numbers that “complete” the diamond based on the Target Trinomial shown at the top.
Look at the Top (Multiply):
Type in the constant c from the equation.
Look at the Bottom (Add):
Type in the coefficient b (the number next to x).
Your Task:
Type two numbers into the Left and Right input boxes that:
Multiply to get the top number.
Add to get the bottom number.
Example: If the top is 12 and the bottom is 7, you would enter 3 and 4 (because 3 × 4 = 12 and 3 + 4 = 7).
Action: Click “Sync Diamond” or press Enter.

Phase 2: Factor Lock
Once you’ve found the two magic numbers, you need to turn them into the final factored form.
The Rule:
If your numbers from Phase 1 were n₁ and n₂, the factored form is (x + n₁)(x + n₂).
Your Task:
Select the button that correctly uses the numbers you just found.
Watch the Signs:
If your number was negative (e.g., -5), the factor will look like (x - 5).
Success:
If you choose correctly, you’ll see “Factor Lock Successful!” and your score will increase.

Tips
Check the Multiples First:
It is usually easier to list pairs of numbers that multiply to the top value first, then check which pair adds up to the bottom.
Sign Rules:
If the Multiply value is positive, both numbers must have the same sign (both + or both -).If the Multiply value is negative, one number must be positive and one must be negative.

This video gives a clear, step-by-step approach to factor trinomials using the diamond method.

• Show Video

 

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

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