Question

Determine o quociente e o resto das divisoes:
a)(2x³-9x²+3x-6):(x-2)
b)(6a³-7a²+2a+1):(3a²-5a+3)

Answer 1

a)(2x³-9x²+3x-6):(x-2)


     2x³-9x²+3x-6                 x-2
-    2x³-4x²                         2x² - 5x - 7                  2x² . (x - 2) = 2x³ - 4x²
      0 -5x²+3x-6                                                   -5x . (x - 2) = -5x² + 10x
     -  (-5)x²+10x                                                    -7 . (x - 2) = -7x + 14
             0   -7x-6
             -  (-7)x +14
                     0 -20

(2x³-9x²+3x-6):(x-2) = (2x² - 5x -7)  resto= -20


b)(6a³-7a²+2a+1):(3a²-5a+3)


    6a³  -7a²   +2a+1          3a²-5a+3
-   6a³ -10a² +6a               2a + 1                 (2a) . (3a²-5a+3) = 6a³-10a²+6a
     0   + 3a² - 4a +1                                         1 . (3a²-5a+3) = 3a² - 5a + 3
        -    3a² - 5a +3
              0       a - 2


(6a³-7a²+2a+1):(3a²-5a+3) = (2a + 1)  resto = (a-2)