3.3B Solving Problems Involving Polynomials

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Presentation transcript:

3.3B Solving Problems Involving Polynomials 3.3 The Box Problem New Math 30-1

Find the value of x that gives the maximum volume. An open box is made by cutting out squares from the corners of a square piece of cardboard and then turning the sides up. x x 30 cm Let x be the side of a small square ( which becomes the height of the box) x 30 - 2x 30 - 2x What are the expressions that represent the dimensions of the box with the largest volume if the piece of cardboard is 30 cm by 30 cm. Find the value of x that gives the maximum volume. What is the maximum volume of the box, to the nearest cubic centimeter? Volume = 2000 cm3 Math 30-1

The volume of the rectangular prism is given by Determine the expressions for the dimensions of the rectangle. Potential Zeros Factor Theorem so (x – 1) is a factor Synthetic Division or Long Division -1 -1 -3 +36 -32 +1 +4 -32 -1 -4 +32 What is the value of x, to the nearest hundredth of a cm, that would give the maximum volume of the box? Vertex at (2.61, 23.7) x = 2.61 cm, max volume is 23.7 cm3 Math 30-1

Assignment Page: 133 Problem Solving 7a,d, 8, 10, 12 Math 30-1