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Pre- Calculus 1. Today’s Agenda – Feb 3. Due TODAY: HW #51 Graphing Polynomials - Redux Due TOMORROW: HW #52 Rational Root Theorem. 1. Silent Do Now. Notes Rational Root Theorem. 3. Work Time. Questions/Summary. SWBAT….
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Pre-Calculus 1 Today’s Agenda – Feb 3 Due TODAY:HW #51 • Graphing Polynomials - Redux Due TOMORROW: HW #52 • Rational Root Theorem • 1. Silent Do Now • Notes • Rational Root Theorem 3. Work Time Questions/Summary SWBAT… • Apply rational root theorem to identify possible roots of a polynomial • Use synthetic/long division or factor theorem to test possible roots
FACTOR THIS… Without more information, our best hope of factoring this cubic function is to guess and check. There is a better way…
The Rational Root Theorem The Rational Root Theorem is a tool for predicting the values of Rational Roots. The theorem says:
Apply theRational Root Theorem Are the coefficients all integers? Then possible rational roots are I where
Apply theRational Root Theorem Factors of constant term, Factors of leading coefficient , All possible rational roots of the form are: I
Apply theRational Root Theorem So the possible zeros are:I
Check with Factor Theorem Substitute each of our possible rational roots into f(x). If the value is a root, then f(value) = 0
Check with Factor Theorem Continue testing possible rational roots for f(x).
Check with Factor Theorem Continue testing possible rational roots for f(x).
Now what? so must be a factor of f(x). Use long or synthetic division to further factor f(x)
Rewrite in Factored Form Simplify! Simplify further!
The Rational Root Theorem The Rational Root Theorem says: