Question

Dividindo o polinomio f(x) =x^3+ x^2 +x+ 1 por g(x) ,obtemos o quociente q(x) =1 +x e o resto r(x) =x+ 1. Determine g(x).

Answer 1

Ola Lidy

f(x) = g(x)*q(x)  + r(x) 

g(x)*q(x) = f(x) - r(x)

g(x) = (f(x) - r(x))/q(x) 

g(x) = (x^3+ x^2 + x + 1 - x - 1)/(x + 1) = x^2*(x + 1)/(x + 1) = x^2