Using Polynomial Long Division to Solve Word Problems in Geometry

This video tutorial teaches how to find one dimension of a rectangular prism given the other two dimensions and either the volume or surface area using polynomial long division. It covers the formulas for volume and surface area, and demonstrates the process of solving for height and length through examples.

What is the formula for the volume of a rectangular prism?

• V = L + W + H

• V = L * W

• V = 2 * (L + W + H)

• V = L * W * H

Which of the following represents the surface area of a rectangular prism?

• SA = L + W + H

• SA = 2 * L * W + 2 * L * H + 2 * H * W

• SA = 2 * (L + W + H)

• SA = L * W * H

Given the volume of a prism as 36X^3 + 60X^2 + X - 20, and its length and width as 3X + 4 and 6X + 5 respectively, what is the height?

• 2X + 1

• 2X - 1

• 3X + 1

• 3X - 1

What is the first step in finding the height of a prism using polynomial long division?

• Subtract the width from the length

• Add the length and width

• Divide the volume by the product of length and width

• Multiply the length and width

How is the length of a rectangular prism determined when given the surface area and other dimensions?

• By multiplying the height and width

• By using polynomial long division

• By subtracting the height from the width

• By adding the height and width

If the surface area of a prism is given as 2604X^3 - 208X^2 - 32X - 74, and its height and width are 12X^2 + 5 and 4X - 9 respectively, what is the length?

• 7X - 2

• 8X + 2

• 8X - 2

• 7X + 2

What mathematical technique is used to find one dimension of a rectangular prism when given the other two dimensions and the volume or surface area?

• Polynomial addition

• Polynomial long division

• Polynomial subtraction

• Polynomial multiplication