The volume of rectangular bar is 640 cubic units. The width is 3 units more than the height and the length is 1 unit more than three times the height. Find the dimensions of the bar.
Let the night be H, then width=H+3 and length=3H+1, so volume=640=H(H+3)(3H+1).
H(3H^2+10H+3)=640; 3H^3+10H^2+3H=640, or 3H^3+10H^2+3H-640=0.
By a bit of trial and error, we can find that H=5 satisfies the equation, so we can use synthetic division to reduce the cubic to a quadratic:
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