How do you factor #5n²-20n+5#?

1 Answer
George C.
Mar 15, 2016

Separate out the common factor #5# and complete the square to find:

#5n^2-20n+5=5(n-2-sqrt(3))(n-2+sqrt(3))#

Explanation:

I will make use of the difference of squares identity:

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

with #a=(n-2)# and #b=sqrt(3)#.

#color(white)()#
First separate out the common scalar factor #5#, then complete the square as follows:

#5n^2-20n+5#

#=5(n^2-4n+1)#

#=5(n^2-4n+4-3)#

#=5((n-2)^2-(sqrt(3))^2)#

#=5((n-2)-sqrt(3))((n-2)+sqrt(3))#

#=5(n-2-sqrt(3))(n-2+sqrt(3))#

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