How do you factor #x² - 14x + 9#?

1 Answer
George C.
May 13, 2016

#x^2-14x+9=(x-7-2sqrt(10))(x-7+2sqrt(10))#

Explanation:

One way is to complete the square and use the difference of squares identity:

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

with #a=(x-7)# and #b=2sqrt(10)# as follows:

#x^2-14x+9#

#=(x-7)^2-7^2+9#

#=(x-7)^2-40#

#=(x-7)^2-2^2*10#

#=(x-7)^2-(2sqrt(10))^2#

#=((x-7)-2sqrt(10))((x-7)+2sqrt(10))#

#=(x-7-2sqrt(10))(x-7+2sqrt(10))#

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