Question

me ayudan con estos ejercicios de polinomios
1)Calcula
P(x)-Q(x)=
Q(x)+R(x)=
R(X)-P(X)=

Answer 1

Teniendo los polinomios
$P(x)=2x^{3} +5x^{2} -x+7 \\ Q(x)=-2 x^{3} +4 x^{2} -6x-5 \\ R(x)= x^{4} + \frac{2}{3} x^{3} -4 x^{2} + \frac{3}{4}x$

Resolvamos las operaciones:

$P(x)-Q(x)=2x^{3} +5x^{2} -x+7-(-2 x^{3} +4 x^{2} -6x-5) \\ \\ =2x^{3} +5x^{2} -x+7+2 x^{3} -4 x^{2} +6x+5 \qquad Agrupando \ terminos \\ \\ =\boxed{4 x^{3}+ x^{2} +5x+12}$

$Q(x)+R(x)=-2 x^{3} +4 x^{2} -6x-5+x^{4} + \frac{2}{3} x^{3} -4 x^{2} + \frac{3}{4}x \\ = x^{4}+(-2+ \frac{2}{3}) x^{3}+(-6+ \frac{3}{4})x-5 \\ \boxed{x^{4} - \frac{4}{3} x^{3} - \frac{21}{4}x-5}$

$R(x)-P(x)=x^{4} + \frac{2}{3} x^{3} -4 x^{2} + \frac{3}{4}x-(2x^{3} +5x^{2} -x+7) \\ =x^{4} + \frac{2}{3} x^{3} -4 x^{2} + \frac{3}{4}x-2x^{3} -5x^{2} +x-7 \\ = x^{4}+( \frac{2}{3}-2) x^{3}-9 x^{2} +( \frac{3}{4}+1)x-7 \\ = \boxed{x^{4} - \frac{4}{3} x^{3}-9 x^{2} + \frac{7}{4}x-7}$

Espero te sirva :)