Answer
$-12s^4 \left( s-4 \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
First, get the $GCF$ of the given expression, $
-12s^5+48s^4
.$ Then, divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient. Finally, factor out the $-1$.
$\bf{\text{Solution Details:}}$
The $GCF$ of the constants of the terms $\{
-12,48
\}$ is $
12
.$ The $GCF$ of the common variable/s is the variable/s with the lowest exponent. Hence, the $GCF$ of the common variable/s $\{
s^5,s^4
\}$ is $
s^4
.$ Hence, the entire expression has $GCF=
12s^4
.$
Factoring the $GCF=
12s^4
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
12s^4 \left( \dfrac{-12s^5}{12s^4}+\dfrac{48s^4}{{12s^4}} \right)
.\end{array}
Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
12s^4 \left( -s^{5-4}+4s^{4-4} \right)
\\\\=
12s^4 \left( -s^{1}+4s^{0} \right)
\\\\=
12s^4 \left( -s+4(1) \right)
\\\\=
12s^4 \left( -s+4 \right)
.\end{array}
Factoring out $-1$ from the second factor results to
\begin{array}{l}\require{cancel}
-12s^4 \left( s-4 \right)
.\end{array}
