Question

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

$x^2+12x+20$

Answer 1

Given: $x^2+12x+20$

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

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

i.e., $(6{)}^2$

$\Rightarrow x^2+12x+20$

$=x^2+12x+6^2–6^2+20$

$=x^2+12x+6^2–36+20$

$=(x^2+12x+6^2)-16$

$=(x+6{)}^2–4^2$

$=(x+6+4)(x+6–4)$

$=(x+10)(x+2)$

Hence, $x^2+12x+20=(x+10)(x+2)$