Writing a Polynomial Function

This lesson teaches how to write a polynomial function by analyzing a physical context. It begins with an introduction to polynomial functions, explaining their components such as coefficients and degree. The lesson then transitions to a practical example of creating a box from a piece of cardboard, focusing on deriving a formula for the volume of the box as a function of its height. The process involves cutting squares from the corners and folding the cardboard. Finally, the lesson demonstrates how to express the volume function in standard polynomial form, emphasizing the conversion from factored form.

What is the degree of the polynomial function F(x) = 5x^3 - 7x^2 + 4x + 3.5?

• 3

• 1

• 2

• 4

When creating a box from a piece of cardboard, what is the initial step?

• Calculating the area

• Measuring the volume

• Cutting squares from each corner

• Folding the cardboard

If the height of the box is 1 inch, what would be the new dimensions of the box?

• Length: 12 inches, Width: 8 inches

• Length: 14 inches, Width: 10 inches

• Length: 8 inches, Width: 4 inches

• Length: 10 inches, Width: 6 inches

What is the volume of the box when the height is 2 inches?

• 0 inches cubed

• 96 inches cubed

• 120 inches cubed

• 144 inches cubed

How do you express the volume of the box as a function of height?

• V(h) = (14 - 2h)(10 - 2h)h

• V(h) = 14h + 10h + h

• V(h) = 14h * 10h * h

• V(h) = 14h - 10h + h

What is the standard form of the polynomial function for the box's volume?

• V(h) = 4h^3 - 48h^2 + 140h

• V(h) = 4h^2 - 48h + 140

• V(h) = 4h^3 + 48h^2 - 140h

• V(h) = 4h^3 - 48h + 140

What is a common misunderstanding about the polynomial function derived for the box's volume?

• It is in standard form

• It is not a polynomial function

• It is a linear function

• It cannot be factored