How do you factor #(x^2-5)#?

1 Answer
George C.
Oct 29, 2015

#x^2-5 = (x-sqrt(5))(x+sqrt(5))#

Explanation:

The difference of squares identity can be written:

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

In order to treat #x^2-5# as a difference of squares, we need to recognise that #5 = (sqrt(5))^2#, then we find:

#x^2-5 = x^2-(sqrt(5)^2) = (x-sqrt(5))(x+sqrt(5))#

In other words, we let #a=x# and #b=sqrt(5)#

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