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Solving

Site: Clare-Gladwin RESD
Course: Michigan Algebra II KHauck
Book: Solving
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Date: Saturday, November 23, 2024, 1:06 AM

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Table of contents

Solving

When solving polynomials, it is helpful to turn the polynomial into its linear factors. This can be accomplished by dividing, as shown in the last lesson, or by factoring. If the polynomial cannot be solved using either of these ways, it is sometimes helpful to use the quadratic formula.

Example 1 Solve the following polynomial: solving_ex1-1 .

Step 1. Set the equation equal to zero.

solving_ex1-2

Step 2. Factor, if possible.

solving_ex1-3

Step 3. Use the Zero Product Property to set each expression equal to zero and solve.

solving_ex1-4

*Note: This problem could have been solved by first factoring out the GCF.

Example 2

Solve the following polynomial:

solving_ex2-1
Step 1 . Determine if there is a monomial that can be divided out of each term.

Since each term in the equation is divisible by 4x, divide this term out first.

solving_ex2-2

Step 2. Factor the remaining expression, if possible.

Since it is not possible to factor the remaining quadratic, use the quadratic formula.

solving_ex2-3

Step 3. Use the Zero Product Property to set the remaining expressions equal to zero.

solving_ex2-32

The final answer is solving_ex2-4


Example 3

Solve the following polynomial:

solving_ex3

Step 1. Set the equation equal to zero.

solving_ex3-1

Step 2. Factor if possible.

Since this polynomial has 4 terms, factor by grouping is needed.

solving_ex3-2

Step 3. Use the Zero Product Property to set the remaining expressions equal to zero.

solving_ex3-3_fix

To learn more about solving polynomials, select the following link:

Solve Polynomials by Factoring

Video Lesson

To learn how to solve polynomials by factoring, select the following link:

Solving Polynomials

Guided Practice

To solidify your understanding of solving polynomials, visit the following link to Holt, Rinehart and Winston Homework Help Online. It provides examples, video tutorials and interactive practice with answers available. The Practice and Problem Solving section has two parts. The first part offers practice with a complete video explanation for the type of problem with just a click of the video icon. The second part offers practice with the solution for each problem only a click of the light bulb away.

Guided Practice

Practice

Solve Polynomials Worksheet

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Answer Key

Solve Polynomials Answer Key

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Sources

Sources used in this book:

CliffsNotes.com. Solving Equations by Factoring. 10 Aug 2010
<http://www.cliffsnotes.com/study_guide/topicArticleId-38949,articleId-38898.html>.

Embracing Mathematics, Assessment & Technology in High Schools; a Michigan Mathematics & Science Partnership Grant Project

Holt, Rinehart & Winston, "Polynomial Functions." http://my.hrw.com/math06_07/nsmedia/homework_help/alg2/alg2_ch06_05_homeworkhelp.html (accessed 810/2010).