Very urgent!

**blertta** · September 30th 2008, 12:45 PM

I have 2 problems. I know that they're too easy but I don't know why my brain it's not working well.
Divide the polynoms:
1) X^6-1 : (x-1)
2) x^4-4x^3+6x^2-4x-15 : (x-1)

Any help will be appreciated!

**Moo** · September 30th 2008, 12:52 PM

Hello,

Originally Posted by blertta

I have 2 problems. I know that they're too easy but I don't know why my brain it's not working well.
Divide the polynoms:
1) X^6-1 : (x-1)

$\frac{x^6-1}{x-1}$ : recognize the formula of a geometric series.

2) x^4-4x^3+6x^2-4x-15 : (x-1)

$=(x^4-x^3)-(3x^3-3x^2)+(3x^2-3x)-(x-1)-16$

**icemanfan** · September 30th 2008, 01:01 PM

Do you know how to do long division of polynomials? For example, take $\frac{x^3 - 2x^2 + 3x - 2}{x - 1}$ .

How many times does $x - 1$ go into $x^3$ ?

$x^2$ times. So, take $x^2(x - 1) = x^3 - x^2$ and subtract that from $x^3 - 2x^2 + 3x - 2$ .
You should get $-x^2 + 3x - 2$ .

How many times does $x - 1$ go into $-x^2$ ?

$-x$ times. So, take $-x(x - 1) = -x^2 + x$ and subtract it from $-x^2 + 3x - 2$ . You should get $2x - 2$ .

How many times does $x - 1$ go into $2x$ ?

Twice. So take $2(x - 1) = 2x - 2$ and subtract it from $2x - 2$ and you are done.

The final result of the division is $x^2 - x + 2$ .

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