Question

Factorize each of the following quadratic polynomials by using the method of completing the square:
a² + 2a − 3

Answer 1

$$\begin{gathered} a^2+2a-3 \\ =a^2+2a+{\left(\frac{2}{2}\right)}^2-{\left(\frac{2}{2}\right)}^2-3[Addingandsubtracting{\left(\frac{2}{2}\right)}^2,thatis,1^2] \\ =a^2+2a+1^2-1^2-3 \\ =(a+1{)}^2-4[Completingthesquare] \\ =(a+1{)}^2-2^2 \\ =\left[\right(a+1)-2]\left[\right(a+1)+2] \\ =(a+1-2)(a+1+2) \\ =(a-1)(a+3) \end{gathered}$$