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Perfect Square Trinomial Calculator.

Test ax² + bx + c for a repeated root.

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01

Set your values

Results update as you type.

Perfect-square trinomial: yes

Perfect-square trinomial

yes
Discriminant: 0

Discriminant

0.000000
Repeated root: 3

Repeated root

0.000000

Results update automatically as you type.

Use Cases

Check homework answers

Verify if a quadratic you factored is indeed a perfect square trinomial, saving time and reducing errors.

Example: Check if x^2 + 6x + 9 is a perfect square trinomial.

Simplify algebraic expressions

Quickly identify perfect square trinomials to rewrite them as squared binomials, which can simplify further calculations.

Example: Recognize 4x^2 + 12x + 9 as (2x + 3)^2.

Frequently Asked Questions

What is a perfect square trinomial?
A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, like (ax + b)^2. It has the form a^2x^2 + 2abx + b^2. This calculator checks if your quadratic fits that pattern.
How do I use this calculator?
Enter the coefficients a, b, and c from your quadratic equation ax^2 + bx + c. The calculator will determine if it is a perfect square trinomial and show the result.
What if my quadratic is not a perfect square trinomial?
The calculator will indicate that it is not a perfect square trinomial. You can still factor it using other methods, but this tool specifically checks for that special pattern.

Tips & Common Mistakes

Tips

  • Ensure you enter the coefficients in the correct order: a (x^2 coefficient), b (x coefficient), and c (constant).
  • Remember that a perfect square trinomial has the form (ax + b)^2 = a^2x^2 + 2abx + b^2, so check if b^2 = 4ac.
  • Use this calculator to double-check your factoring work, especially when dealing with large numbers.
  • If the calculator says it's not a perfect square trinomial, try factoring by other methods like grouping or the quadratic formula.

Common Mistakes to Avoid

  • Entering the coefficients in the wrong order, such as swapping b and c.
  • Forgetting to include negative signs for coefficients, which can affect the result.
  • Assuming any trinomial with a perfect square constant is a perfect square trinomial; the middle term must also match the pattern.

Last updated: August 13, 2026