Applied Practice with
Multiplying Polynomials

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Answer the following questions that utilize polynomials in their solutions:

1. A rectangular swimming pool is twice as long as it is wide.  A small concrete walkway surrounds the pool.  The walkway is a constant 2 feet wide and has an area of 196 square feet.  Find the dimensions of the pool.

 

 Answer#1 

 

 

2. Think of a number.  Subtract 7.  Multiply by 3.  Add 30.  Divide by 3.  Subtract the original number.  The result is always 3.  Use polynomials to illustrate this number trick.

Answer#2
 

   

 

3. The side of a cube is represented by x + 1.  Find, in terms of x, the volume of the cube.

 

 Answer#3 

 

 

4. Let an integer be represented by x.  Find, in terms of x, the product of three consecutive integers starting with x.

 

 Answer#4 

 

 

5. Write a variable expression for the area of a square whose side is x + 8.

 

Answer#5 

 


 
6.

The length of a rectangular window is 5 feet more than its width, w.  The area of the window is 36 square feet.  Which equation could be used to find the dimensions of the window?

Choose: