💎 Diamond Problem Calculator
Solve the diamond problem for factoring
How to Use This Calculator
Select Mode
Choose to find factors or verify all values.
Enter Known Values
Fill in the known values in the diamond. Top = sum, Bottom = product.
Solve
Click to find the missing values or verify your entries.
The Diamond Problem
Find two numbers (left and right) such that:
left + right = top (sum)
left × right = bottom (product)
Example 1: Top = 7, Bottom = 12
Find two numbers that add to 7 and multiply to 12
Answer: left = 3, right = 4 (or vice versa)
Check: 3 + 4 = 7 ✓, 3 × 4 = 12 ✓
Example 2: Top = 5, Bottom = -6
Find two numbers that add to 5 and multiply to -6
Answer: left = -1, right = 6
About Diamond Problem Calculator
The Diamond Problem is a visual tool for factoring quadratic expressions. It helps you find two numbers given their sum and product, which is essential for factoring trinomials. The diamond shape makes it easy to visualize the relationships.
When to Use This Calculator
- Factoring Trinomials: Find two numbers for x² + bx + c
- Quadratic Equations: Break down middle term
- Algebra Problems: Solve sum and product puzzles
Why Use Our Calculator?
- ✅ Visual Tool: See diamond structure
- ✅ All Solutions: Find all possible factor pairs
- ✅ Verification: Check your work
- ✅ Educational: Learn diamond method
- ✅ Free Tool: No registration
Connection to Factoring
For factoring x² + bx + c, the diamond problem finds numbers m and n such that m + n = b and m × n = c. Then x² + bx + c = (x + m)(x + n).
Frequently Asked Questions
What is the diamond problem?
A visual method to find two numbers given their sum and product, used for factoring quadratics.
How does it relate to factoring?
For x² + bx + c, you need two numbers that add to b and multiply to c. The diamond finds these numbers.
Can there be multiple solutions?
Yes! Sometimes there are multiple pairs that satisfy the sum and product conditions.