Answer:
2[tex]w^{3}[/tex]-6[tex]w^{2}[/tex]+4w=240
Step-by-step explanation:
The length and height are given in terms of the width. Width =w; Length =(2w−4); Height =(w−1); and the Volume is equal to the product of the three. Therefore, we can set up the equation as follows:
w×(2w−4)×(w−1)=240
To finish, we distribute and combine like terms:
(2[tex]w^{2}[/tex]−4w)×(w−1)=240
2[tex]w^{3}[/tex]−2[tex]w^{2}[/tex]−4[tex]w^{2}[/tex]+4w=240
2[tex]w^{2}[/tex]−6[tex]w^{2}[/tex]+4w=240
Therefore, 2[tex]w^{3}[/tex]−6[tex]w^{2}[/tex]+4w=240 is our equation for the dimensions of the dumpster in terms of w.
