Applied Practice with
Multiplying Polynomials

Topic Index | Algebra Index | Regents Exam Prep Center

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.





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.




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





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





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





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?