The document discusses how to factor "unfactorable" quadratic trinomials using the technique of completing the square. It explains that completing the square involves changing the trinomial into a perfect square trinomial form (x + p)2 by first dividing by the leading coefficient, rewriting in standard form, taking half the coefficient of x and squaring it and adding it to both sides, and then extracting the square root to reveal the factored form. The document provides step-by-step instructions for using this technique to factor quadratic trinomials.

1. Completing the Square Factoring “unfactorable” 2 nd degree trinomials Don Simmons © D. T. Simmons, 2009

2. Completing the Square We have learned earlier that a perfect square trinomial can always be factored. Therefore, if we have a trinomial we cannot factor using integers, we can change it in such a way that we are dealing with a perfect square trinomial. © D. T. Simmons, 2009

3. Completing the Square Recall that a perfect square trinomial is always in the form: Therefore, we have to change the polynomial so that it fits the form. To get the most out of this presentation, use pencil and paper and work through the instructions slowly and carefully. © D. T. Simmons, 2009

4. Completing the Square The equation we are going to solve is the following… By testing whether or not the factors of c can sum to equal b, we can determine if the trinomial is factorable . This trinomial is not factorable in its present form. © D. T. Simmons, 2009

5. Step 1 Divide by the leading coefficient to set the a- value to 1. © D. T. Simmons, 2009

6. Step 2 Re-write the equation in the form ax + by = c © D. T. Simmons, 2009

7. Step 3 Find one-half of the b value. Add the square of that number to both sides. © D. T. Simmons, 2009

8. Step 4 Re-write the perfect square trinomial as a binomial squared. Find the square root of each side of the equation. © D. T. Simmons, 2009

9. Step 5 Solve for x . © D. T. Simmons, 2009

10. Try it. You’ll like it! That’s all folks! © D. T. Simmons, 2009