Question

Factorize each of the following quadratic polynomials by using the method of completing the square:
p² + 6p − 16

Answer 1

\[p^2 + 6p - 16\]
\[ = p^2 + 6p + \left( \frac{6}{2} \right)^2 - \left( \frac{6}{2} \right)^2 - 16 [\text{ Adding and subtracting }\left( \frac{6}{2} \right)^2 ,\text{ that is }, 3^2 ]\]
\[ = p^2 + 6p + 3^2 - 9 - 16\]
\[ = (p + 3 )^2 - 25 [\text{ Completing the square }]\]
\[ = (p + 3 )^2 - 5^2 \]
\[ = [(p + 3) - 5][(p + 3) + 5]\]
\[ = (p + 3 - 5)(p + 3 + 5)\]
\[ = (p - 2)(p + 8)\]