Question

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

Answer 1

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