Question

a rectangle prism has a volume of 3x^2 + 18x+ 24. its base has a length of x + 2 and width of 3, what expression represents the height of the prism

Answer 1

$\bf \textit{volume of a rectangular prism}\\\\ V=lwh\qquad \begin{cases} l=x+2\\ w=3\\ V=3x^2 + 18x+ 24 \end{cases}\implies \cfrac{V}{lw}=h \\\\\\ \cfrac{3x^2 + 18x+ 24}{3(x+2)}=h\implies \cfrac{\underline{3}(x^2 + 6x+ 8)}{\underline{3}(x+2)}=h \\\\\\ \cfrac{(x+4)\underline{(x+2)}}{\underline{(x+2)}}=h\implies x+4=h$