Question

Factorize each of the following quadratic polynomials by using the method of completing the square:
z² − 4z − 12

Answer 1

$$\begin{gathered} z^2-4z-12 \\ =z^2-4z+{\left(\frac{4}{2}\right)}^2-{\left(\frac{4}{2}\right)}^2-12[Addingandsubtracting{\left(\frac{4}{2}\right)}^2,thatis,2^2] \\ =z^2-4z+2^2-2^2-12 \\ =(z-2{)}^2-16[Completingthesquare] \\ =(z-2{)}^2-4^2 \\ =\left[\right(z-2)-4]\left[\right(z-2)+4] \\ =(z-6)(z+2) \end{gathered}$$