Evaluate a polynomial using the Remainder Theorem.Use the Factor Theorem to deal with a polynomial equation.Use the Rational Zero Theorem to discover rational zeros.Find zeros of a polynomial function.Use the Linear Factorization Theorem to find polynomials via provided zeros.Use Descartes’ Rule of Signs.Solve real-world applications of polynomial equations


You are watching: How to find zeros of a polynomial function

A brand-new bakery offers decorated sheet cakes for children’s birthday parties and also other distinct occasions. The bakery desires the volume of a little cake to be 351 cubic inches. The cake is in the form of a rectangular solid. They desire the size of the cake to be 4 inches longer than the width of the cake and the height of the cake to be one-3rd of the width. What have to the dimensions of the cake pan be?

This problem deserve to be solved by composing a cubic function and fixing a cubic equation for the volume of the cake. In this area, we will certainly comment on a range of devices for writing polynomial functions and solving polynomial equations.


Examining a Polynomial Using the Remainder Theorem

In the last section, we learned how to divide polynomials. We deserve to currently use polynomial department to evaluate polynomials utilizing the Remainder Theorem. If the polynomial is divided by

*


Analysis

We deserve to examine our answer by evaluating

*
is a variable of the polynomial. We can usage the Division Algorithm to compose the polynomial as the product of the divisor and also the quotient:


We deserve to variable the quadratic variable to write the polynomial as


By the Factor Theorem, the zeros of

*
has actually integer coefficients, then eextremely rational zero of
*
has actually the form
*
whereis a variable of the constant term
*
andis a element of the leading coefficient
*

When the leading coeffective is 1, the possible rational zeros are the components of the constant term.




See more: Why Do Dogs Put Their Head On You Rs, Why Does My Dog Rest Their Head On Me

Given a polynomial function

*
use the Rational Zero Theorem to find rational zeros.

Determine all components of the constant term and also all determinants of the leading coefficient.Determine all feasible values of
*
whereis a factor of the consistent term andis a factor of the leading coreliable. Be certain to incorporate both positive and negative candidays.Determine which possible zeros are actual zeros by evaluating each situation of
*