Directions: Answer these questions pertaining to factoring polynomials. Choose the best answer. Check your answer when finished.

1.

The area of a larger rectangle is 6a(4a + 3) and the area of a smaller rectangle is 5(4a + 3). What is the difference of the areas, in factored form?

2.

Kyle calls to tell you that he has found the correct factors to the homework problem dealing with the difference of two squares. Which of the following could he possibly tell you is his answer? (Assume his answer is correct!)

3.

Given: 6x^{3} - 10x^{2} - 8x and 2x(3x^{2} - 5x - 4).
Let y_{1} =
6x^{3} - 10x^{2} - 8x and y_{2} = 2x(3x^{2} - 5x - 4).

If you graph each function, how will the graphs appear, and why?

4.

You use the TABLE feature on your graphing calculator to examine the graphs from Question #3. How does the table of values for y_{1} compare with the table of values for y_{2} ?

5.

A ceremonial red carpet is rectangular in shape and covers 2x^{2} + 11x + 12 square feet. If the width of the carpet is (x + 4) feet, express the length, in feet.

6.

You are playing a game of "Deal-A-Math" and you draw the card shown below. What is the correct response?

7.

a. A teacher sees the following factoring on a student's paper. Is this factoring correct?

b. What is the value of 4(x - 3)^{2} - 8(x - 3) - 4(x - 3)(x - 5)?

8.

Which of the following expressions cannot be used to express the area of the blue shaded regions of this rectangle?

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