Precalc Unit 2 Pwr, Polynomial, Rational Functions.notebook

1

October 09, 2018

Feb 1­5:33 AM

HOMEWORK: pp. 104­107,

#3, 16, 26, 27, 40, 80, 85, 98, 102, 110, 111

Feb 1­5:33 AM

HOMEWORK: pp. 104­107,

#3, 16, 26, 27, 40, 80, 85, 98, 102, 110, 111

Precalc Unit 2 Pwr, Polynomial, Rational Functions.notebook

2

October 09, 2018

Feb 1­5:33 AM

2.3 Remainder and Factor Theorems

Lesson Objectives:

1) I can apply synthetic division and long division to polynomial division problems

2) I can use the Remainder and Factor Theorems

Oct 8­3:23 PM

What could this polynomial's equation be?

Precalc Unit 2 Pwr, Polynomial, Rational Functions.notebook

3

October 09, 2018

Oct 7­8:17 PM

linear

quadratic

cubic

quartic

5th degree

6th degree

7th degree

1 possible root

2 possible roots

3 possible roots

4 possible roots

5 possible roots

6 possible roots

7 possible roots

Oct 7­8:17 PM

single roots

double roots

triple roots

ex: (x­4)(x­2)(x+1)=0

x=4, x=2, x=­1

each root has a multiplicity of 1

ex: (x­4)2=0

x=4, 4 has a multiplicity of 2 (it is a repeated zero)

graph is tangent to x­axis at that point

ex: (x­4)3=0

x=4, 4 has a multiplicity of 3 (it is a repeated zero)

the graph crosses the x­axis at that point

MULTIPLICITY: (x­c)m­ when (x­c) is a factor of a polynomial function­c is a zero of multiplicity m of f, where m is a natural #

Precalc Unit 2 Pwr, Polynomial, Rational Functions.notebook

4

October 09, 2018

Aug 2­3:02 PM

Perform the following using LONG DIVISION (not a calculator)

5 1 7 2 3

Nov 2­8:11 AM

***

***f(x)/d(x)=q(x)+ ; so, f(x)=d(x)*q(x) + r(x); if r(x)=0, then d(x) divides evenly into f(x) and is, therefore, a FACTOR of f(x)!*****

Long division of polynomials is the

SAME PROCESS!! Let's Try this one together

Precalc Unit 2 Pwr, Polynomial, Rational Functions.notebook

5

October 09, 2018

Nov 2­8:11 AM

Nov 2­8:11 AM

Precalc Unit 2 Pwr, Polynomial, Rational Functions.notebook

6

October 09, 2018

Aug 2­3:42 PM

Factor completely (using the given factor and polynomial long division)...you MIGHT want to factor the quotient, since, if you are given a factor, your remainder will be zero, and if you don't factor the quotient, you won't have factored completely!!!

A) x3+7x2+4x­12; x+6 B) 6x3­2x2­16x­8; 2x­4