Question

dividindo f(x) por X²+x, obtemos o quociente q(x)=X²-x-2 e resto r(x)=7 x-1 obtenha o polinômio f(x)

Answer 1

P(X) = f(X) . q(X) + r(X)
P(X) = (x2 + x) . (x2 - x -2) + 7x - 1
P(X) = x4 - x3 -2x2 + x3 -x2 - 2x +7x - 1
P(X) = x4 -3x2 +5x -1

Answer 2

f (x) ÷ x^2 + x
7 X - 1 x^2 -X - 2
(×^2 +X ) . (x^2 - X - 2 ) + 7 X - 1
x^4 - x^3 - 2 X ^2 + X ^3 - x^2 - 2 X
x^4 - 2 X^2 -x^2 - 2 X + 7x - 1
x^4 - 3x^2 + 5 X - 1