Frequently Asked Questions
What is completing the square?
Rewriting ax^2 + bx + c as a(x + b/2a)^2 + (c - b^2/4a). The first piece is a perfect square trinomial scaled by a; the second piece is a constant remainder.
Are all squares of binomials perfect square trinomials?
Yes. Conversely, every perfect square trinomial is the square of some binomial. The names are used interchangeably.
What is the discriminant role?
If b^2 - 4ac = 0, the quadratic has a double root, the parabola touches the x-axis at exactly one point, and the trinomial factors as a perfect square.
How do you factor a perfect square trinomial?
A perfect square trinomial a² ± 2ab + b² factors as (a ± b)². Check that the first and last terms are perfect squares and the middle term equals twice the product of their roots; then the sign of the middle term sets the sign inside the binomial.
What is the difference between a perfect square trinomial and a difference of squares?
A perfect square trinomial has three terms, a² + 2ab + b², and factors as (a + b)². A difference of squares has two terms, a² − b², and factors as (a + b)(a − b). One is a square, the other a product of conjugates.
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