Question

Factorizar

$3x^{4} yx^{5} zx^{2} +9x^{2} yz^{3} -12x^{5} y^{2} z$

Answer 1

Facto-rizar

$3x^4yx^5zx^2+9x^2yz^3-12x^5y^2z$

$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \:a^b\cdot \:a^c=a^{b+c}$

$x^5x^4x^2=\:x^{4+5+2}=\:x^{11}$

$=3x^{11}yz+9x^2yz^3-12x^5y^2z$

$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \:a^{b+c}=a^ba^c$

$x^{11}=x^2x^9,\:z^3=zz^2,\:x^5=x^2x^3,\:y^2=yy$

$3x^2x^9yz+9x^2yzz^2-12x^2x^3yyz$

$\mathrm{Reescribir\:como}$

$=3x^9x^2yz+3\cdot \:3x^2yz^2z-3\cdot \:4x^3x^2yyz$

$\mathrm{Factorizar\:el\:termino\:comun\:}3x^2yz$

$=3x^2yz\left(x^9-4x^3y+3z^2\right)$