Polynomial Review OBJ: SWBAT analyze and graph polynomials

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

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

Analyzing Standard Form Con’t.d  End Behavior PositiveNegative Even Odd

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

Factored Form F(x) = a(x – f 1 ) n (x – f 2 ) n ….. Where…. Degree: LC: Y-int: **

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

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

Synthetic Division Example  Divide 3x 3 – 2x by x + 1

Tips to Finding Roots 1) Descartes Theorem: 2) Rational Roots Theorem 3) Use division to verify

Example f(x) = x 3 – x 2 – 25x + 25

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

Example f(x) = x 4 – x 3 – 21x 2 + x + 20