Question

Se p(x) = x³ - 5 x e r (x) = -x³ - x² + x + 3, obtenha q(x) tal que p(x) + q(x) = r(x)

Answer 1

$\displaystyle p(x)=x^3-5x\\\\r(x)=-x^3-x^2+x+3\\\\p(x)+q(x)=r(x)\implies (x^3-5x)+r(x)=-x^3-x^2+x+3\\q(x)=-x^3-x^2+x+3-x^3+5x=-x^3-x^3-x^2+5x+x+3=\\-2x^3-x^2+6x+3\\\\\boxed{q(x)=-2x^3-x^2+6x+3}$