Answer
The factor of the polynomial $3{{x}^{2}}-48$ is$3\left( x+4 \right)\left( x-4 \right)$.
Work Step by Step
$3{{x}^{2}}-48$
The factor of the polynomial $3{{x}^{2}}-48$ is calculated as follows.
$3{{x}^{2}}-48=3{{x}^{2}}-3\cdot 16$
Use the distributive property, $a\cdot \left( b+c \right)=a\cdot b+a\cdot c$, to get,
$\begin{align}
& 3{{x}^{2}}-48=3{{x}^{2}}-3\cdot 16 \\
& =3\left( {{x}^{2}}-16 \right) \\
& =3\left( {{x}^{2}}-{{4}^{2}} \right)
\end{align}$
Use the identity ${{A}^{2}}-{{B}^{2}}=\left( A-B \right)\left( A+B \right)$;
$3{{x}^{2}}-48=3\left( x+4 \right)\left( x-4 \right)$
