Polynomials

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Identifying the Multiplicties

Odd: when the graph crosses the x-axis at the zero

Even: when the graph intersects but does not cross the x-axis at the zero.

How to Solve a Polynomial

Complex you use the Conjugate Zeros Theorem.

Given two real zeros: do synthetic division once, get a new polynomial, then do synthetic division with the remaining zero and new polynomial

If given none: graph the equation, finding the zeros from the x-intercepts, and then use synthetic division.

Given a real zero: you use synthetic division.

Students: Alex Goodreau Alicia Ashton Alyssa Molnar

Identifying of Number of Zeros

Complex: a polynomial f(x) of degree n, with n is greater than or equal to one, has at least one complex zero

Real: a polynomial of degree n has at most n distinct zeros

Identidying the Degree of a Polynomial

End Behavior

odd degree

even degree

"+" l.c.

"-" l.c.

By turning points: the degree can be up to one more than the number of turning points

By zeros: the degree can be up to the same number of x-intercepts on the graph

Definitions

Polynomial: an expression of two or more algebraic terms

Leading coefficient: a number, which is multiplies the highest non-zero power of the independent variable in a polynomial function.

End Behavior: The appearance of a graph as it is followed farther and farther in either direction.

Turning Points: when the graph changes from increasing to dec reasing and vice versa.

X-intercepts: the point where the graph crosses the x-axis