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Classwork
Opening Exercise
Find the following quotients, and write the quotient in standard form.
Exercise 1
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.
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