Part 2 - Practice Factoring Using the Root Rules: Graph the polynomial in your calculator: f (a) = 24 + 5x3 - 221x2 - 2181x - 5124 Identify what locations on the graph of f(x) have integer roots and list them. Use synthetic division to divide by those obvious roots! Show what the polynomial above would look like in factored form - using all the factors you found from the synthetic division. Explain how you use each of the 7 points below to run analysis on your polynomial. Remember, on a test, I will not be taking your calculator away, so practice using your calculator to identify the integer roots before you do anything crazy. (You must be able to do this graphing analysis moving forward.) General Strategy for factoring high ordered polynomials 1. Use the Fundamental Theorem of Algebra to find how many roots are buried in your function. (The highest ordered exponent is also the number of roots of the equation. Some of the roots may be complex, meaning they have an imaginary part.) 2. Remember: Complex Conjugates Theorem. (Imaginary roots ALWAYS come in pairs) [just like shoes - a left and right one] 3. Use the Rational Roots Theorem to make a list of all possible roots.[p/q] 4. Especially if the equation has a lot of potential rational roots, use Descartes Rule of Signs to find out the maximum number of possible, positive, rational roots. (Rational roots are always real roots, because rational numbers are a subset of real numbers. These real roots are places where the graph of the function crosses the x-axis). 5. Use the Polynomial Remainder Theorem. (This theorem will quickly identify some rational roots, start working through the possible roots found in step 3 above. Keep going until you only have 2 left. Now go to step 6.) 6. Use synthetic division to divide f(x) by one root after another. You'll be left with just a quadratic function from those last 2 roots you didn't identify. Now go to step 7. 7. Solve the remaining quadratic function by any means you can: inspection, complete the square, or quadratic formula. That should get you to a clean list of roots for any polynomial. If you have a graphing calculator & (such as Desmos), graph the equation to see if your roots are correct. If factoring a high ordered polynomial is a homework assignment and your teacher allows it[Sarah Adams does allow it], use the graphing calculator before you even start. Then you know where the path leads. Excerpt taken from: Math Coaching Feel free to follow the link for additional step-by-step information on how to work through all the rules in chapter 3. Post your final work here as a picture or a pdf or a word doc, as usual. Let me know if you have any questions along the