Answer
$x^2(x+5)(x+1)
$
Work Step by Step
Factoring the $GCF=
x^2
,$ the given expression, $
x^4+6x^3+5x^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
x^2(x^2+6x+5)
.\end{array}
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
x^2(x+5)(x+1)
.\end{array}
Let
\begin{array}{l}\require{cancel}Y_1=
x^4+6x^3+5x^2
\text{ and }\\Y_2=
x^2(x+5)(x+1)
.\end{array}
Using a graphing calculator, the graph of $Y_1$ (dotted red graph) and $Y_2$ (solid blue graph) are given below. Since the two graphs coincide, then $Y_2$ and $Y_1$ are the same. That is, $Y_2$ is the correct factored form of $Y_1.$
