Mastery Check Solutions

Show What You Know

Wallies Warehouse needs to refinish the front of their building. The total surface area is needed for the project. The surface area of just the door is 2x square meters and the area of each window is $x^{2}$ square meters.

What is the total area of the front of the building, excluding the door and windows?

$A_{square} = b h; b = h = 2 x A_{square} = (2 x) (2 x) A_{square} = 4 x^{2}$

$A_{rectangle} = b h; b = (3 x + 2), h = (2 x + 5) A_{rectangle} = (3 x + 2) (2 x + 5) A_{rectangle} = 6 x^{2} + 15 x + 4 x + 10 A_{rectangle} = 6 x^{2} + 19 x + 10$

$\begin{array}{rcl} Total Area & = & square + rectangle - (door + 3 windows) \\ Total Area & = & 4 x^{2} + (6 x^{2} + 19 x + 10) - (2 x + 3 x^{2}) \\ = & 10 x^{2} + 19 x + 10 - 2 x - 3 x^{2} \\ = & 7 x^{2} + 17 x + 10 \end{array}$

Note

Remember that the total area will be found by adding the area of each part of the building, and then subtracting the door and windows. Talking through or making note of your plan first can be helpful.

Q: How many quadrilaterals do you need the area for? Explain.
A: 6, the square, rectangle, door, and 3 windows

The volume of a standard size box in Wallies Warehouse is given in cubic centimeters.

Factor to find the dimensions of the box.

$15 x^{3} + 405 15 (x^{3} + 27) 15 (x + 3) (x^{2} - 3 x + 9)$

The dimensions of the box are 15 cm, $(x + 3)$ cm, and $(x^{2} - 3 x + 9)$ cm.

Note

Q: Is it possible to specifically name the length, width, and height once the dimensions are determined? Explain.
A: No, not enough information is provided.

Say What You Know

In your own words, talk about what you have learned using the objectives for this part of the lesson and your work on this page.

Note

Restate the objectives of the lesson in your own words. If you are unable to restate the lesson objectives, go back and reread the objectives and then explain them.

Determine if an expression represents a polynomial.
Add, subtract, and multiply to simplify polynomial expressions.
Factor polynomial expressions.
Factor the sum and difference of cubes.