Perfect Square Trinomial Calculator

Perfect Square Trinomial Calculator

Check whether a quadratic expression is a perfect square trinomial and see the factored form when it is.

Last updated: March 2026 | By ForgeCalc Engineering

Trinomial Factor Solver

Algebra check

Analysis Steps

1.Trinomial: 1x^2 + 6x + 9
2.Check the discriminant: b^2 - 4ac
3.b^2 = 6^2 = 36
4.4ac = 4 x 1 x 9 = 36
5.Discriminant = 0
6.This trinomial is a perfect square trinomial.
Factored Form
(1x + 3)^2

Discriminant: 0

What a Perfect Square Trinomial Means

A perfect square trinomial is a quadratic expression that factors into the square of a binomial. It is closely tied to the discriminant being zero.

How to Check a Perfect Square Trinomial

  1. Confirm the first and last coefficients are positive.
  2. Compute the discriminant b^2 - 4ac.
  3. If the discriminant is zero, the trinomial is a perfect square trinomial.
  4. Write the matching squared binomial form if needed.
discriminant = b^2 - 4ac

Worked Example

Example: x^2 + 6x + 9 factors as (x + 3)^2.

b^2 - 4ac = 6^2 - 4(1)(9) = 0

Frequently Asked Questions

Can the middle term be negative?

Yes. The binomial may be a subtraction, which gives a negative middle term.

Do the first and last terms have to be perfect squares?

Yes, for the trinomial to factor cleanly as a squared binomial.

Does this accept decimals?

Yes. Any finite real coefficients are accepted.

What does a zero discriminant mean?

It means the trinomial has a repeated root and can be written as a square.

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