ANSWER
The factorization of [tex]100x^2-20x+1[/tex]
is [tex](10x-1)^2[/tex].
EXPLANATION
We want to factor [tex]100x^2-20x+1[/tex]
Comparing this to [tex]ax^2+bx+c[/tex]
[tex]a=100,b=-20,c=1[/tex]
[tex]ac=100[/tex]
We look for factors of 100 that add up to [tex]-20[/tex].
These factors are [tex]-10,-10[/tex]
We now split the middle term to obtain;
[tex]100x^2-10x-10x+1[/tex]
We factor to obtain;
[tex]10x(10x-1)-1(10x-1)[/tex]
This simplifies to [tex](10x-1)(10x-1)=(10x-1)^2[/tex]
