Question

factorizar, usando el factor común polinomio:​

Answer 1

Respuesta:

$1) \mathrm{Factorizar}\:a\left(x+1\right)+b\left(x+1\right):\quad \left(1+x\right)\left(a+b\right)\\\\\mathrm{Factorizar\:el\:termino\:comun\:}\left(1+x\right)\\\\=\left(1+x\right)\left(a+b\right)$

$2)\mathrm{Factorizar}\:m\left(2a+b\right)+p\left(2a+b\right):\quad \left(b+2a\right)\left(m+p\right)\\\\\mathrm{Factorizar\:el\:termino\:comun\:}\left(b+2a\right)\\\\=\left(b+2a\right)\left(m+p\right)$

$3)\mathrm{Factorizar}\:x^2\left(p+q\right)+y^2\left(p+q\right):\quad \left(p+q\right)\left(x^2+y^2\right)\\\\\mathrm{Factorizar\:el\:termino\:comun\:}\left(p+q\right)\\\\=\left(p+q\right)\left(x^2+y^2\right)$

$\mathrm{Factorizar}\:\left(a^2+1\right)-b\left(a^2+1\right):\quad \left(a^2+1\right)\left(1-b\right)\\\\\mathrm{Factorizar\:el\:termino\:comun\:}\left(a^2+1\right)\\\\=\left(a^2+1\right)\left(1-b\right)$

$5)\mathrm{Factorizar}\:\left(1-x\right)+5c\left(1-x\right):\quad \left(1-x\right)\left(1+5c\right)\\\\\mathrm{Factorizar\:el\:termino\:comun\:}\left(1-x\right)\\\\=\left(1-x\right)\left(1+5c\right)$

$6) \mathrm{Factorizar}\:a\left(2+x\right)-\left(2+x\right):\quad \left(2+x\right)\left(a-1\right)\\\\\mathrm{Factorizar\:el\:termino\:comun\:}\left(2+x\right)\\\\=\left(2+x\right)\left(a-1\right)$

$7)\mathrm{Factorizar}\:\left(x+y\right)\left(n+1\right)-3\left(n+1\right):\quad \left(1+n\right)\left(x+y-3\right)\\\\\mathrm{Factorizar\:el\:termino\:comun\:}\left(1+n\right)\\\\=\left(1+n\right)\left(x+y-3\right)$

$8)\mathrm{Factorizar}\:\left(a+1\right)\left(a-1\right)-2\left(a-1\right):\quad \left(a-1\right)^2\\\\\mathrm{Factorizar\:el\:termino\:comun\:}\left(a-1\right)\\\\=\left(a-1\right)\left(a+1-2\right)\\\\\mathrm{Simplificar\:}a+1-2:\quad a-1\\\\=\left(a-1\right)^2$

Espero te ayude :"3.