Question

Determina el resto de dividir: {( x – 1 )6 . ( x – 2 )5 + 1 } : ( x – 3 )

Answer 1

Explicación paso a paso:

$\mathrm{Desarrollar\:}\left(x-1\right)\cdot \:6\left(x-2\right)\cdot \:5+1:\quad 30x^2-90x+61\\\\30x^2-90x+61=x-3\\\\\mathrm{Sumar\:}3\mathrm{\:a\:ambos\:lados}\\\\30x^2-90x+61+3=x-3+3\\\\\mathrm{Simplificar}\\\\30x^2-90x+64=x\\\\\mathrm{Restar\:}x\mathrm{\:de\:ambos\:lados}\\\\30x^2-90x+64-x=x-x\\\\\mathrm{Simplificar}\\\\\mathrm{Simplificar}\\\\\mathrm{Para\:una\:ecuacion\:de\:segundo\:grado\:de\:la\:forma\:}ax^2+bx+c=0\mathrm{\:las\:soluciones\:son\:}$$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$\mathrm{Para\:}\quad a=30,\:b=-91,\:c=64:\quad x_{1,\:2}=\frac{-\left(-91\right)\pm \sqrt{\left(-91\right)^2-4\cdot \:30\cdot \:64}}{2\cdot \:30}\\\\x=\frac{-\left(-91\right)+\sqrt{\left(-91\right)^2-4\cdot \:30\cdot \:64}}{2\cdot \:30}:\quad \frac{91+\sqrt{601}}{60}\\\\x=\frac{-\left(-91\right)-\sqrt{\left(-91\right)^2-4\cdot \:30\cdot \:64}}{2\cdot \:30}:\quad \frac{91-\sqrt{601}}{60}\\\\Las\:soluciones\:a\:la\:ecuacion\:de\:segundo\:grado\:son:$$x=\frac{91+\sqrt{601}}{60},\:x=\frac{91-\sqrt{601}}{60}$

Espero te sirva, saludos.