## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$-x^3(x-1)(x-3)$
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}