Question

Factorize each of the following quadratic polynomials by using the method of completing the square: $p^2+6p+8=0$

Answer 1

Given: $p^2+6p+8=0$

Step 1: $\frac{1}{2}\left(6p\right)=3p$

Step 2: $(3{)}^2=9$

Step 3: $p^2+6p+8+9=0+9$

$\Rightarrow (p^2+6p+9)+8=9$

$\Rightarrow (p+3{)}^2=9-8$

$\Rightarrow (p+3{)}^2=1$

$\Rightarrow p+3=\pm 1$

$\Rightarrow p=1-3$ or $p=-1-3$

$\therefore p=-2,-4$

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