Writing about pattern in long polynomial division

[kryms3n]

Man I am really confused about this
will someone help me out

WRITING ABOUT MATH
Finding Patterns in Polynomial Division

Complete the following polynomial divisions:

a. (x^2 - 1) divided by (x-1) =

b. (x^3 - 1) divided by (x-1) =

c. (x^4 - 1) divided by (x-1) =

Write a brief description of the pattern that you obtain, and use your result to find a formula for the polynomal division (x^n - 1)/(x - 1). Create a numerical example to test your formula.

I know how to do the polynomial division. But what is the formula in the paragraph part?

 

[stapel]

What are the results of your divisions? What are your thoughts regarding what you see?

Please be specific. Thank you.

Eliz.

 

[kryms3n]

okay

okay
well i dont really know what the pattern is


but the solutions are
for
a. (x +1)
b. (x^2 + x + 1)
c. (x + 1) (x^2 +1)

im not sure how to get it into the formula
i see that (x +1) is in the even exponents

but i dont see how odd goes with it....

thatz how im confused

 

[Goistein]

If n is a power of 2, then use difference of squares, and factor to divide by X-1. That's as far as my A2 class taught with dividing. Well maybe synthetic division would help...

 

[stapel]

a. (x +1)
b. (x^2 + x + 1)
c. (x + 1) (x^2 +1)

The result for (c) should have been x³ + x² + x + 1.

Note:

. . . . .n = 2: x¹ + x⁰

. . . . .n = 3: x² + x¹ + x⁰

. . . . .n = 4: x³ + x² + x¹ + x⁰

Follow the pattern.

Eliz.