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

Positive Negative

Even

Odd

Example

f(x) = 7x5 – 2x2 + 9Deg: ____LC: ____Y-int: ____E.B.: ____# roots: ____# extrema: ____

Factored Form

F(x) = a(x – f1)n(x – f2)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 3x3 – 2x2 + 6 by x + 1

Tips to Finding Roots

1) Descartes Theorem:

2) Rational Roots Theorem

3) Use division to verify

Example

f(x) = x3 – x2 – 25x + 25

Steps to Graphing

1)2)3)4)5)

Example

f(x) = x4 – x3 – 21x2 + x + 20