# How do you factor #5n²-20n+5#?

##### 1 Answer

Mar 15, 2016

Separate out the common factor

#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

First separate out the common scalar factor

#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))#