Solve p(x)=2x3+x2-4x-3 using rational roots theorem

Answered: Solve p(x)=2x3+x2-4x-3 using rational…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Solve p(x)=2x³+x²-4x-3 using rational roots theorem

Expert Solution

Step 1: information

The rational roots theorem states that

"A rational root of a polynomial function $bold italic f bold left parenthesis bold italic x bold right parenthesis bold equals bold italic a subscript bold n bold italic x to the power of bold n bold plus bold italic a subscript bold n bold minus bold 1 end subscript bold italic x to the power of bold n bold minus bold 1 end exponent bold plus bold. bold. bold. bold plus bold italic a subscript bold 1 bold italic x bold plus bold italic a subscript bold 0$ is of the form

$bold p over bold q equals fraction numerator bold italic a bold space bold italic f bold italic a bold italic c bold italic t bold italic o bold italic r bold space bold italic o bold italic f bold space bold italic t bold italic h bold italic e bold space bold italic c bold italic o bold italic n bold italic s bold tan bold italic t over denominator bold italic a bold space bold italic f bold italic a bold italic c bold italic t bold italic o bold italic r bold space bold italic o bold italic f bold space bold italic t bold italic h bold italic e bold space bold italic l bold italic e bold italic a bold italic d bold italic i bold italic n bold italic g bold space bold italic c bold italic o bold italic e bold italic f bold italic f bold italic i bold italic c bold italic i bold italic e bold italic n bold italic t end fraction$ "