MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C8196E.08B33B80" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C8196E.08B33B80 Content-Location: file:///C:/AFA88E92/PolynomialFunctionsUnitTwoARR.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Creating Polynomial Functions (Equations) from Rational Roots - Unit= (2)

Creating Polynomial Functions (Equations) from Rational Roots

 

***********= *********************************

 

Given Rational Roots:           ( – 3 )  ,  ( + 1/2 )  ,=   ( + 4 )

 

        &= nbsp;           &nbs= p;  

 

        &= nbsp;           &nbs= p;          -4      -3      -2      -1       0     +1    +2      +3     +4

 

Roots:        X =3D –3      = ;            &n= bsp;       X =3D +1/2   X =3D +4

 

Factors:  ( X + 3 )           &nb= sp;            =        ( 2x – 1 )     = ;     ( X – 4 )

 

Equat= ion (Function):    Y =3D = + 2X3 – 3X2 – 23X + 12

&nb= sp;

Changing all signs generates an equivalent = but negative polynomial:  Y =3D – 2X3<= /sup> + 3X2 + 23X – 12

&nb= sp;

To do th= is opposite (­–) generation change all signs of (x) terms  then  to check factor the equation.

 

<= o:p> 

***********= *********************************

 

Given Rational Roots:           ( – 2 )  ,  (– 2/3 )  ,=   ( + 3 )

 

        &= nbsp;           &nbs= p;  

 

       &n= bsp;                -4        -3     -2      -1       0    +1      +2     +3   +4

 

Roots:       X =3D=   – 2           X = =3D  –2/3    X =3D +3

 

Factors:  ( X + 2 )           &nb= sp;            =        ( 3x + 2 )      = ;    ( X – 3 )

 

Equat= ion (Function):   Y =3D= + 3X3 – X2 – 20X – 12

 

Changing all signs generates an equivalent = but negative polynomial:  Y =3D – 3X3<= /sup> + X2 + 23X + 12

&nb= sp;

To do th= is opposite (­–) generation change all signs of (x) terms  then  to check factor the equation.

 

***********= *********************************

 

Approaching Polynomial Fun= ctions, using a nontraditional  method ( using roots to generate equations)

allows students to deminis= h the mystery behind Polynomials Functions and where they originated.

 

This backdoor approach also provides, a much needed review in multiplication of algebraic expressions:<= /p>

(Bionomials and Trinomials= ) which many students need at this stage of their Mathematics development.

 

Tom Love        =             &nb= sp;           Malone College        =             &nb= sp;        Fall 2007

 

 

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Tom Love=         =             &nb= sp;       Malone College        =             &nb= sp;      Fall 2003

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