Como vocĂȘ fatora # x ^ 2 + 8x + 12 #?

Responda:

#x^2+8x+12=color(green)((x+2)(x+6))#

Explicação:

Em geral
#color(white)("XXX")(x^2+(color(red)(a)+color(blue)(b))x+color(red)(a)*color(blue)(b))=(x+color(red)(a))(x+color(blue)(b))#

#8 = color(red)(2)+color(blue)(6)#
e
#12=color(red)(2)*color(blue)(6)#

So
#x^2+8x+12#

#color(white)("XXX")=(x^2+(color(red)(2)+color(blue)(6))x+color(red)(2)*color(blue)(6)#

#color(white)("XXX")=(x+color(red)(2))(x+color(blue)(6))#