Polynomial Review

1. Polynomial Review OBJ: SWBAT analyze and graph polynomials

2. Definition Definition: A polynomial function is a function where…. Terms:

3. Analyzing Standard Form F(x) = Key Info: Degree: Leading Coefficient: Y-intercept: # roots: # extrema:

4. Analyzing Standard Form Con’t.d • End Behavior

5. Example f(x) = 7x5 – 2x2 + 9 Deg: ____ LC: ____ Y-int: ____ E.B.: ____ # roots: ____ # extrema: ____

6. Factored Form F(x) = a(x – f1)n(x – f2)n….. Where…. Degree: LC: Y-int: **

7. Example: f(x) = -2(x – 3)2(x + 4)4(2x – 1)2 Deg: ____ LC: ____ Y-int: ____ E.B.: ____ # roots: ____ # extrema: ____ Roots: ____

8. X-intercepts • X-intercepts = roots = zeroes • If k is a root, then f(k) = 0 or (x – k) is a factor • How to determine: • Synthetic or Long Division

9. Synthetic Division Example • Divide 3x3 – 2x2 + 6 by x + 1

10. Tips to Finding Roots • Descartes Theorem: • Rational Roots Theorem • Use division to verify

11. Example f(x) = x3 – x2 – 25x + 25

12. Steps to Graphing 1) 2) 3) 4) 5)

13. Example f(x) = x4 – x3 – 21x2 + x + 20