Question

dado os polinômios f(x)= -x³+4x²-5x e g(x)=x²-1, calcule:​

Answer 1

$f(x) = -x^3 + 4x^2 - 5x\\g(x) = x^2 - 1$

a)

$f(x) + g(x) = -x^3 + 4x^2 - 5x + (x^2 - 1)\\f(x) + g(x) = -x^3 + 4x^2 - 5x + x^2 - 1\\f(x) + g(x) = -x^3 + 5x^2 - 5x - 1$

b)

$f(x) * g(x) = (-x^3 + 4x^2 - 5x) * (x^2 - 1)\\f(x) * g(x) = -x^5 + x^3 + 4x^4 - 4x^2 - 5x^3 + 5x\\f(x) * g(x) = -x^5 + 4x^4 + x^3 - 5x^3 - 4x^2 + 5x\\f(x) * g(x) = -x^5 + 4x^4 - 4x^3 - 4x^2 + 5x$

c)

$f(x) - g(x) = (-x^3 + 4x^2 - 5x) - (x^2 - 1)\\f(x) - g(x) = -x^3 + 4x^2 - 5x - x^2 + 1\\f(x) - g(x) = -x^3 + 4x^2 - x^2 - 5x + 1\\f(x) - g(x) = -x^3 + 3x^2 - 5x + 1$