Question

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

$p^2+6p+8$

Answer 1

Given: $p^2+6p+8$

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

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

i.e., $(3{)}^2$

$\Rightarrow p^2+6p+8$

$=p^2+6p+3^2–3^2+8$

$=[p^2+6p+3^2]-9+8$

$=(p+3{)}^2–1$

$=(p+3{)}^2–1^2$

$=(p+3–1)(p+3+1)$

$=(p+2)(p+4)$

Hence, $p^2+6p+8=(p+2)(p+4)$