Polinômios

Sejam  e  . Tomando r(x) como sendo o resto na divisão de p(x) por q(x) , o valor de r(2) será :   Resp : E

a) -8
b) -6
c) -4
d) -3
e) -2

Olá.

 2x^{2010}  - 5x² - 13x + 7                         |x² + x + 1
-2x^{2010} - 2x^{2009} - 2x^{2008}           2x^{2008} - 2x^{2007} + 2x^{2006} - ... - 2x³ + 2x - 7
                  -2x^{2009} - 2x^{2008} - 5x² - 13x + 7
                   2x^{2007} + 2x^{2008} + 2x^{2007}
                                                      2x^{2007} - 5x² -13x + 7
                                                     -2x^{2007} - 2x^{2006} - 2x^{2005}
                                                                       -2x^{2006} - 2x^{2005} - 5x² - 13x + 7
                                                                       .
                                                                       .
                                                                       .
                                                                       -2x^5 - 2x^4 - 5x² - 13x + 7
                                                                        2x^5 + 2x^4 + 2x³
                                                                                            2x³ - 5x² - 13x + 7
                                                                                           -2x³ - 2x² - 2x 
                                                                                                  -7x² - 15x + 7
                                                                                                   7x² + 7x + 7
                                                                                                         -8x + 14 --> R(x)

R(2) = -8*2 + 14 .:. R(2) = -16 + 14 .:. R(2) = -2

Att.,
Pedro