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!
Do you know how to do long division of polynomials? For example, take $\displaystyle \frac{x^3 - 2x^2 + 3x - 2}{x - 1}$.
How many times does $\displaystyle x - 1$ go into $\displaystyle x^3$?
$\displaystyle x^2$ times. So, take $\displaystyle x^2(x - 1) = x^3 - x^2$ and subtract that from $\displaystyle x^3 - 2x^2 + 3x - 2$.
You should get $\displaystyle -x^2 + 3x - 2$.
How many times does $\displaystyle x - 1$ go into $\displaystyle -x^2$?
$\displaystyle -x$ times. So, take $\displaystyle -x(x - 1) = -x^2 + x$ and subtract it from $\displaystyle -x^2 + 3x - 2$. You should get $\displaystyle 2x - 2$.
How many times does $\displaystyle x - 1$ go into $\displaystyle 2x$?
Twice. So take $\displaystyle 2(x - 1) = 2x - 2$ and subtract it from $\displaystyle 2x - 2$ and you are done.
The final result of the division is $\displaystyle x^2 - x + 2$.