Question

Dividindo-se o polinômio f(x) por x² + x+1, obtemos o quociente q(x)= x² - x e o resto r(x)= -x+13. Determine f(x).

Answer 1

quociente * divisor + resto = dividendo

então
$Q(x)*D(x)+R(x) =f(x)$

Q(x) = quociente = x²-x
D(x) = divisor = x²+x+1
r(x) = resto = -x+13

$(x^2-x)*(x^2+x+1)+(-x+13)= f(x)\\\\ (x^4+\not x^3+\not x^2-\not x^3-\not x^2-x) -x+13 =f(x)\\\\x^4-x -x +13 = f(x)\\\\x^4-2x+13 = f(x)$