Question

Factorize each of the following quadratic polynomials by using the method of completing the square:
x² + 12x + 20

Answer 1

$$\begin{gathered} x^2+12x+20 \\ =x^2+12x+{\left(\frac{12}{2}\right)}^2-{\left(\frac{12}{2}\right)}^2+20[Addingandsubtracting{\left(\frac{12}{2}\right)}^2,thatis,6^2] \\ =x^2+12x+6^2-6^2+20 \\ =(x+6{)}^2-16[Completingthesquare] \\ =(x+6{)}^2-4^2 \\ =\left[\right(x+6)-4]\left[\right(x+6)+4] \\ =(x+6-4)(x+6+4) \\ =(x+2)(x+10) \end{gathered}$$