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