Answer
$p=\left\{ -4,4 \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Express the given equation, $
4p^2-16=0
,$ in factored form. Then, use the Zero-Factor Property by equating each factor to zero. Finally, solve each equation.
$\bf{\text{Solution Details:}}$
The factored form of the equation above is
\begin{array}{l}\require{cancel}
4(p^2-16)=0
\\\\
4(p+4)(p-4)=0
\\\\
\dfrac{4(p+4)(p-4)}{4}=\dfrac{0}{4}
\\\\
(p+4)(p-4)=0
.\end{array}
Equating each factor to zero (Zero-Factor Property), then
\begin{array}{l}\require{cancel}
p+4=0
\text{ OR }
p-4=0
.\end{array}
Using the properties of equality to solve each of the equation above results to
\begin{array}{l}\require{cancel}
p+4=0
\\\\
p=-4
\\\\\text{ OR }\\\\
p-4=0
\\\\
p=4
.\end{array}
Hence, the solutions are $
p=\left\{ -4,4 \right\}
.$
$\bf{\text{Supplementary Solution/s:}}$
Factoring the $GCF=
4
,$ the expression, $
4p^2-16
,$ above is equivalent to
\begin{array}{l}\require{cancel}
4 \left( \dfrac{4p^2}{4}-\dfrac{16}{4} \right)
\\\\=
4 \left( p^2-4 \right)
.\end{array}
Using the factoring of the difference of $2$ squares which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
4(p+4)(p-4)
.\end{array}