Check whether ax² + bx + c is a perfect square trinomial
A perfect square trinomial is produced by squaring a binomial. The first term must be the square of px, the last term must be the square of q, and the middle term must be twice the product of those two base terms. Checking these three pieces helps determine whether a quadratic can be written in compact squared form, which is useful for factoring and completing the square.
A perfect square trinomial is created by squaring a binomial. Recognizing the pattern helps factor quadratics quickly and supports completing-the-square work.
The first and last terms must be square terms.
The middle coefficient must equal 2pq or -2pq.
The last term q² is non-negative because it is a square.
The sign inside (px±q)² follows the sign of the middle term.
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