Complete the following questions to model and solve polynomial functions for rea

Question

Complete the following questions to model and solve polynomial functions for real-life examples. Make sure you sketch a picture or graph of the problem situation, labeling appropriately and then show your work - all the steps - that led you to your solution.:

1) A company%u2019s profits, in thousands of dollars, is given by p(x) = x3 + x2 %u2013 10x + 5, where x is the number of years since its start. What was the profit for year 7?

2) A candle mold shaped like a rectangular prism has a square base. Its height is 5 centimeters longer than its width. The mold has a volume of 144 cubic centimeters. How wide is the mold? (Volume of a rectangular prism = lwh)

3) Joe forms a box without a top by cutting squares of equal size from the corners of a piece of cardboard measuring 10 centimeters by 8 centimeters. After removing the squares, he folds up the sides. Write and graph the function that gives the volume of the box, where x is the side length of a square Joe removes. Use the graph to estimate the greatest possible volume.

Explanation / Answer

1) p(x) = x3 + x2 %u2013 10x + 5
then p(7)-p(6)=7^3+7^2-10(7)+5 - 6^3+6^2-10(6)+5
=327-197= 130

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