How do you factor #x^2 - 12x + 34#?

1 Answer
George C.
Aug 30, 2016

#x^2-12x+34=(x-6-sqrt(2))(x-6+sqrt(2))#

Explanation:

Complete the square then use the difference of squares identity:

#a^2-b^2=(a-b)(a+b)#

with #a=(x-6)# and #b=sqrt(2)# as follows:

#x^2-12x+34#

#=x^2-12x+36-2#

#=(x-6)^2-(sqrt(2))^2#

#=((x-6)-sqrt(2))((x-6)+sqrt(2))#

#=(x-6-sqrt(2))(x-6+sqrt(2))#

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