Question

Factorize the following quadratic polynomial by using the method of completing the square:

$a^2+2a-3$

Answer 1

Given: $a^2+2a-3$

Since, the coefficient of $a^2$ is unity.

$\therefore$ Adding and subtracting $(\frac{1}{2}\times$ coefficient of $a{)}^2$

i.e., $(1{)}^2$

$\Rightarrow a^2+2a-3$

$=a^2+2a+1^2–1^2-3$

$=(a^2+2a+1^2)–4$

$=(a+1{)}^2–2^2$

$=(a+1+2)(a+1–2)$

$=(a+3)(a–1)$

Hence, $a^2+2a-3=(a+3)(a–1)$