Polynomials

Mere som dette

MAT.116 1.1-1.3

af David Kedrowski

Library and Information Science by means of Buddhist way

af Penpan Pecharas

Attitude And Behavior

af Lara El Bachouti

Types of Navigation

af Júlia Motger

Polynomials

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