How do you factor $5n²-20n+5$ ?

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Answer 1 · 2016-03-15T22:21:00

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

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

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:

$5n^2-20n+5$

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

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

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

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

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

How do you factor 5n²-20n+55n²-20n+5?