### Home > A2C > Chapter 13 > Lesson 13.1.2 > Problem13-36

13-36.
1. Josephina thinks that she has discovered a new pattern, shown below. 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 probably need “, …,” in the middle of your expression.

x − 1 = 1(x − 1)

x2 − 1 = (x + 1) (x − 1)

...

$\frac{x^5-1}{x-1}=x^4+x^3+x^2+x+1$

Check by multiplying, as in part (a).

$\frac{x^n-1}{x-1}=?$