## Intermediate Algebra (6th Edition)

$2x^3(5x+1)(2x+5)$
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}