Precalc Unit 2 Pwr, Polynomial, Rational Functions.notebook
Transcript of Precalc Unit 2 Pwr, Polynomial, Rational Functions.notebook
Precalc Unit 2 Pwr, Polynomial, Rational Functions.notebook
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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
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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
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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
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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
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October 09, 2018
Nov 28:11 AM
Nov 28:11 AM
Precalc Unit 2 Pwr, Polynomial, Rational Functions.notebook
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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