Question

Aiuda pa hoy pls :c

Efectúa la siguiente Sustracción de polinomios:

1) F(x) - G(x)

$F(x)= 2x^{4} +3x^{3} -4x^{2} +6x-5\\G(x)= -4x^{5}-3x^{2}+2x-3$

2) P(x) - Q(x)
$P(x)= \frac{1}{2} x^{5} -\frac{2}{3}x^{3}+\frac{1}{3}x^{2} \\\\Q(x)= \frac{3}{4}x^{5} -\frac{1}{6}x^{3}+\frac{2}{9}x^{2}-\frac{1}{5}$

Answer 1

Respuesta:

1) $4x^5+2x^4+3x^3-x^2+4x-2$

2) $\displaystyle-\frac{1}{4}x^5-\frac{3}{6}x^3+\frac{1}{5}$

Explicación paso a paso:

1)

$(2x^4+3x^3-4x^2+6x-5)-(-4x^5-3x^2+2x-3)\\\\2x^4+3x^3-4x^2+6x-5+4x^5+3x^2-2x+3$

agrupo términos semejantes.

$4x^5+2x^4+3x^3+(-4x^2+3x^2)+(6x-2x)+(-5+3)$

resuelvo.

$4x^5+2x^4+3x^3-x^2+4x-2$

2)

$\displaystyle\frac{1}{2}x^5-\frac{2}{3}x^3+\frac{1}{3}x^2-\left(\frac{3}{4}x^5-\frac{1}{6}x^3+\frac{2}{9}x^2-\frac{1}{5} \right) \\\\\frac{1}{2}x^5-\frac{2}{3}x^3+\frac{1}{3}x^2-\frac{3}{4}x^5+\frac{1}{6}x^3-\frac{2}{9}x^2+\frac{1}{5}\\\\\left(\frac{1}{2}x^5-\frac{3}{4}x^5 \right)+\left(-\frac{2}{3}x^3+\frac{1}{6}x^3 \right)+\left(\frac{1}{3}x^2-\frac{2}{9}x^2 \right)+\frac{1}{5}$

$\displaystyle\left(\frac{2}{4}x^5-\frac{3}{4}x^5 \right)+\left(-\frac{4}{6}x^3+\frac{1}{6}x^3 \right)+\left(\frac{1}{3}x^2-\frac{1}{3}x^2 \right)+\frac{1}{5} \\\\-\frac{1}{4}x^5-\frac{3}{6}x^3+\frac{1}{5}$