Question

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

Answer 1

p(x) + q(x) = r(x)
⇒[-p(x)] + p(x) + q(x)= r(x) + [-p(x)]
⇒ [p(x) - p(x)] + q(x) = r(x) + [-p(x)]
⇒ [0] + q(x) = r(x) - p(x)
⇒ q(x) = r(x) + [-p(x)]
 
[-p(x)] = (-1) × [p(x)] = - p(x) = - (x³ -5x) = -x³ + 5x

q(x) = r(x) + [-p(x)] = (-x³ - x² + x + 3) + (-x³ + 5x) = x³[-1+(-1)] + x²(-1+0) + x(1+5) + (3+0) = -2x³ - x² + 6x + 3

q(x) = -2x³ - x² + 6x + 3