The polynomial function to find the volume of the tray is [tex]4x^{3} -30x^{2} +50x[/tex] cubic inches.
According to the question,
We have the following information:
Christina cuts 4 squares with side length x inches from the corners of a 5 inch by 10 inch cardboard rectangle. She folds the remaining cardboard to make a tray that is x inches high.
Now, the length of the tray will be (10-2x) inches and the breadth of the tray will be (5-2x) inches.
Volume of tray = length*breadth*height
Volume of tray = (10-2x)(5-2x)x
Volume of tray = x(50-20x-10x+4[tex]x^{2}[/tex])
Volume of tray = x(4[tex]x^{2}[/tex]-30x+50)
Volume of tray = [tex]4x^{3} -30x^{2} +50x[/tex] cubic inches
Hence, the polynomial function to find the volume of the tray is [tex]4x^{3} -30x^{2} +50x[/tex] cubic inches.
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