Perfect Square Trinomials
Completion requirements
Perfect Square Trinomials
When a perfect square trinomial is written in the form \(ax^2 + bx + c\), and \(a = 1\), the following patterns emerge, as seen in the Investigation.
- \(c\) is always the square of one-half of the coefficient of the middle term, or \(c = \left( {\frac{b}{2}} \right)^2 \).
- The factors are always in the form \(\left( {x + \frac{b}{2}} \right)\left( {x + \frac{b}{2}} \right) = \left( {x + \frac{b}{2}} \right)^2 \).
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Perfect Square Trinomials
In general, a perfect square trinomial with \(a = 1\) is
\(ax^2 + bx + c = x^2 + 2rx + r^2 = \left( {x + r} \right)^2 \), where \(r = \frac{b}{2}\)
\(ax^2 + bx + c = x^2 + 2rx + r^2 = \left( {x + r} \right)^2 \), where \(r = \frac{b}{2}\)