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Home > INT3 > Chapter 10 > Lesson 10.2.2 > Problem 10-125

10-125.
  1. 10-125. Josephina thinks that she has discovered a new pattern, shown at right. Homework Help ✎

    1. Check her equations by multiplying. Does her pattern work?

    2. Based on her pattern, what does equal? Is it true? Justify your answer.

    3. Make a conjecture about how to represent the result for . You will need “…” in the middle of your expression.

To check a division problem using multiplication, multiply the divisor by the quotient. In the second case, multiply (x − 1)(x + 1). Does it equal x2 − 1? How will you check the third and fourth cases?

Look for a pattern in the quotients. Look at the number of terms and the exponent on each term.