Perfect Square Trinomial Calculator

Check whether ax² + bx + c is a perfect square and factor it.

Perfect square? (1=yes, 0=no) 1

Square-root binomial constant 3

Formula: Perfect square ⟺ b² = 4ac (and a, c ≥ 0)

Step-by-step with your numbers:

1. Values used:

2. a = 1

3. b = 6

4. c = 9

6. Perfect square? (1=yes, 0=no) = 1

7. Square-root binomial constant = 3

Did we solve your problem today?

A perfect square trinomial factors as (√a·x + k)². This tool tests for that and finds k.

The math behind it

ax² + bx + c is a perfect square when b² = 4ac. Then it equals (√a·x + b/(2√a))².

x² + 6x + 9: b² = 36 = 4·1·9, so it is a perfect square = (x + 3)².

What if b² ≠ 4ac?

It is not a perfect-square trinomial; factor it another way or use the quadratic formula.