Dividing by 𝒙 − 𝒂 and by 𝒙 + 𝒂


Related Topics:
Lesson Plans and Worksheets for Algebra II
Lesson Plans and Worksheets for all Grades
More Lessons for Algebra
Common Core For Algebra




Share this page to Google Classroom

Dividing by 𝒙 − 𝒂 and by 𝒙 + 𝒂

Student Outcomes

  • Students work with polynomials with constant coefficients to prove polynomial identities.

New York State Common Core Math Algebra II, Module 1, Lesson 6

Worksheets for Algebra 2

Classwork

Opening Exercise

Find the following quotients, and write the quotient in standard form.

Exercise 1

  1. Use patterns to predict each quotient. Explain how you arrived at your prediction, and then test it by applying the reverse tabular method or long division.

Example 1 What is the quotient of (𝑥2−𝑎2)/(𝑥−𝑎)? Use the reverse tabular method or long division

Exercises 2–4 2. Work with your group to find the following quotients. 3. Predict without performing division whether or not the divisor will divide into the dividend without a remainder for the following problems. If so, find the quotient. Then check your answer. 4. a. Find the quotient for 𝑛 = 2, 3, 4, and 8
b. What patterns do you notice?
c. Use your work in part (a) to write an expression equivalent to

Lesson Summary

Based on the work in this lesson, it can be concluded that the following statements are true for all real values of 𝑥 and 𝑎:

𝑥2 − 𝑎2 = (𝑥 − 𝑎)(𝑥 + 𝑎)
𝑥3 − 𝑎3 = (𝑥 − 𝑎)(𝑥2 + 𝑎𝑥 + 𝑎2)
𝑥3 + 𝑎3 = (𝑥 + 𝑎)(𝑥2 − 𝑎𝑥 + 𝑎2),

and it seems that the following statement is also an identity for all real values of 𝑥 and 𝑎: 𝑥𝑛 − 1 = (𝑥 − 1)(𝑥𝑛 − 1 + 𝑥𝑛 − 2 + 𝑥𝑛 − 3 + ⋯ + 𝑥1 + 1), for integers 𝑛 > 1.




Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

Fraction Concoction Game



We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.