The X method (also called the diamond method or X game) solves trinomial factoring instantly. Enter your product and sum — get both missing numbers with full steps.
The X method is a factoring technique where you draw a large X (or diamond) shape, write the product (A × B) at the top and the sum (A + B) at the bottom, then find the two numbers A and B that satisfy both conditions. Those numbers become the factors in the binomial form (x + A)(x + B).
You may know this same method as the diamond method, diamond problem, or X game — different teachers and curricula use different names, but the math is identical. The diamond problem solver handles all three versions instantly.
Name used in many US high school curricula. The shape is drawn as a large X with two diagonal lines crossing. Product goes at the top of the X, sum at the bottom.
Same technique — shape drawn as a rotated square (diamond). Common in CPM (College Preparatory Mathematics) curriculum. Identical structure, different visual orientation.
Informal name used by students and some teachers. Identical structure to the X method and diamond method — fill in the missing two numbers from the product and sum.
All three use the same rule: top = product (A × B), bottom = sum (A + B). This calculator works for all three.
Five steps — works for any trinomial, including negatives.
Identify b and c in x² + bx + c. The X method uses c as the top value (product) and b as the bottom value (sum) in the X diagram.
Draw your X shape. Place c (the product A × B) at the top and b (the sum A + B) at the bottom. The left and right sections hold the unknowns.
Find two numbers A and B where A × B = top value AND A + B = bottom value. Apply sign rules: same signs if product is positive, opposite signs if negative. Also works for factor diamond problems.
The trinomial factors as (x + A)(x + B). If A or B is negative, the sign is included in the binomial — e.g. (x − 2)(x − 3) when A = −2 and B = −3.
Expand (x + A)(x + B) using FOIL. You should recover the original trinomial exactly. If not, recheck your sign rules or factor pairs.
Three worked examples using the X method.
Top = 12, bottom = 7 → A = 3, B = 4
Both factors negative (positive product, negative sum) → A = −2, B = −3
Opposite signs (negative product) → larger positive: A = 4, B = −3