Question

If the volume of the rectangular prism is represented by 6x2 – 2x + 8 and the base area is 2x – 4, which expression represents the height?

Answer 1

$\bf \textit{volume of a rectangular prism}\\\\ V=Lwh~~ \begin{cases} L=length\\ w=width\\ h=height\\ \cline{1-1} V=6x^2-2x+8\\ \stackrel{base}{Lw}=2x-4 \end{cases}\implies 6x^2-2x+8=(2x-4)h \\\\\\ \cfrac{6x^2-2x+8}{2x-4}=h\implies \cfrac{\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(3x^2-x+4)}{\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x-2)}=h\implies \cfrac{3x^2-x+4}{x-2}=h$