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TL;DW: How do you know which numbers to test for synthetic division? You use the Rational Roots Theorem! This gives the possible rational roots of any polynomial with integer coefficients. In this clip, we break down f(x) = 2x^4 + 5x^3 - 5x^2 - 5x + 3 to find all possible rational roots. By looking at the factors of the constant term (p = 3) and the leading coefficient (q = 2), we can narrow down our search to just 8 possibilities. The Process: Find factors of the constant term (p). Find factors of the leading coefficient (q). List every possible fraction (p/q). This saves so much time compared to random guessing! #math #algebra2 #precalculus #rationalrootstheorem #polynomials #mathshortcuts #studyhelp #stemeducation #algebra #homeworkhelp Possible RATIONAL ROOTS of Polynomial from Rational Roots Theorem 📖 Precalculus, by Stewart, Redlin, and Watson: https://amzn.to/4sIzIE9. Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn... 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on LinkedIn: / bill-kinney-a1246610 🔴 Follow me on Twitter: / billkinneymath 🔴 Follow me on Instagram: / billkinneymath 🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ 🔴 Desiring God website: https://www.desiringgod.org/ AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.