Answer
$2x^3(5x+1)(2x+5)$
Work Step by Step
Factoring the $GCF=2x^3$, then the given expression, $
20x^5+54x^4+10x^3
$, is equivalent to $
2x^3(10x^2+27x+5)
$.\\
The two numbers whose product is $ac=
10(5)=50
$ and whose sum is $b=
27
$ are $\{
2,25
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
2x^3(10x^2+27x+5)
$, is
\begin{array}{l}\require{cancel}
2x^3(10x^2+2x+25x+5)
\\\\=
2x^3[(10x^2+2x)+(25x+5)]
\\\\=
2x^3[2x(5x+1)+5(5x+1)]
\\\\=
2x^3[(5x+1)(2x+5)]
\\\\=
2x^3(5x+1)(2x+5)
.\end{array}
