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# Completing the square

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A step-by-step instruction about how to complete the square for factoring trinomials.

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### Completing the square

1. 1. Completing the Square Factoring “unfactorable” 2 nd degree trinomials Don Simmons © D. T. Simmons, 2009
2. 2. Completing the Square <ul><li>We have learned earlier that a perfect square trinomial can always be factored. </li></ul><ul><li>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. </li></ul>© D. T. Simmons, 2009
3. 3. Completing the Square <ul><li>Recall that a perfect square trinomial is always in the form: </li></ul><ul><li>Therefore, we have to change the polynomial so that it fits the form. </li></ul><ul><li>To get the most out of this presentation, use pencil and paper and work through the instructions slowly and carefully. </li></ul>© D. T. Simmons, 2009
4. 4. Completing the Square <ul><li>The equation we are going to solve is the following… </li></ul><ul><li>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. </li></ul>© D. T. Simmons, 2009
5. 5. Step 1 <ul><li>Divide by the leading coefficient to set the a- value to 1. </li></ul>© D. T. Simmons, 2009
6. 6. Step 2 <ul><li>Re-write the equation in the form ax + by = c </li></ul>© D. T. Simmons, 2009
7. 7. Step 3 <ul><li>Find one-half of the b value. </li></ul><ul><li>Add the square of that number to both sides. </li></ul>© D. T. Simmons, 2009
8. 8. Step 4 <ul><li>Re-write the perfect square trinomial as a binomial squared. </li></ul><ul><li>Find the square root of each side of the equation. </li></ul>© D. T. Simmons, 2009
9. 9. Step 5 <ul><li>Solve for x . </li></ul>© D. T. Simmons, 2009
10. 10. Try it. You’ll like it! That’s all folks! © D. T. Simmons, 2009