How do you factor $z^2-20z+100$ ?

Question

2686 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-29T12:36:49

See process below

There are several ways to solve

1.- Using cuadratic formula

$az^2+bz+c=0$ and his solutions $z=(-b+-sqrt(b^2-4ac))/(2a)$

In our case

$a=1; b=-20 and c=100$

$z=(20+-sqrt(400-400))/2=20/2=10$ that's double root, so

$(z-10)(z-10)=(z-10)^2$

2.- Using notable identities. In this case

$(a-b)^2=a^2-2ab+b^2$ we have $a=z$ and $b=10$

$(z-10)^2=(z-10)(z-10)=z^2-2·10·z+10^2=z^2-20z+100$

Answer 2 · 2018-03-29T12:38:18

$(z-10)(z-10)$

By sum and product Means that two numbers whose sum is - $20$ and product is 100

= $z^2-10z-10z+100$

= $z(z-10)-10(z-10)$

= $(z-10)(z-10)$

Hope this helps!

How do you factor z^2-20z+100z^2-20z+100?