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

Mar 29, 2018

See process below

#### Explanation:

There are several ways to solve

$a {z}^{2} + b z + c = 0$ and his solutions $z = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

In our case

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

$z = \frac{20 \pm \sqrt{400 - 400}}{2} = \frac{20}{2} = 10$ that's double root, so

$\left(z - 10\right) \left(z - 10\right) = {\left(z - 10\right)}^{2}$

2.- Using notable identities. In this case

${\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}$ 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

Mar 29, 2018

$\left(z - 10\right) \left(z - 10\right)$

#### Explanation:

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

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

=$z \left(z - 10\right) - 10 \left(z - 10\right)$

=$\left(z - 10\right) \left(z - 10\right)$

Hope this helps!