How do you factor #x^2 + 8x + 12#?

1 Answer
Alan P.
Jun 12, 2016

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

Explanation:

In general
#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)#
and
#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))#

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