Question

Doar a) și b)
Arătați rezolvarea, vă rog

Apreciez rsp.​

Answer 1

sper să te ajute :)))))))

Answer 2

$\displaystyle a)~P(X)=X^4+X^3+X^2+X\\\\ Q(X)=X+2$                          

                 $\left\begin{array}{ccc}~~~~~~~~~~~~~~X^4+X^3+X^2+X\\-X^4-2X^3\\~~~~~~~~~------------\\~~~~~~~~~~~~~/~-X^3+X^2+X\\~~~~~~~~~~~~~~X^3+2X^2\\~~~~~~~~~------------\\~~~~~~~~~~~~~~~~~~~~~~~/~~~3X^2+X\\~~~~~~~~~~~~~~~~~~~~~~~~~~-3X^2-6X\\~~~~~~~~~~------------\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~/~~-5X\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~5X+10\\~~~~~~~~~~------------\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~/~~ 10\end{array}\right|\left\begin{array}{ccc}\cfrac{X+2}{X^3-X^2+3X-5} \\\\\\\\\\\\\\\\\\\\\\\\\end{array}\right$                  

$\displaystyle c=X^3-X^2+3X-5\\\\ r=10$

$\displaystyle b)~P(x)=-5X^4-X^3+X^2-2X-6\\\\ Q(X)=X-1$

         $\left\begin{array}{ccc}~~~~~~~~~~~~~~~~-5X^4-X^3+X^2-2X-6\\5X^4-5X^3\\~~~~~~--------------\\~~~~~~~~~~~~~~~/~-6X^3+X^2-2X-6\\~~~~~~~~~6X^3-6X^2\\~~~~~~~--------------\\~~~~~~~~~~~~~~~~~~~~/~-5X^2-2X-6\\~~~~~~~~~~~~~~~~~~~~~5X^2-5X\\~~~~~~~--------------\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~/~~-7X-6\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~7X-7\\~~~~~~~~--------------\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~/~-13\end{array}\right|\left\begin{array}{ccc}\cfrac{X-1}{-5X^3-6X^2-5X-7}\\\\\\\\\\\\\\\\\\\\\\\\\end{array}\right$

$\displaystyle c=-5X^3-6X^2-5X-7\\\\r=-13$