Rewrite the expression so that the GCF is factored completely, algebra homework help

1. An expression is shown below:

3x3y + 12xy - 3x2y - 12y

Part A: Rewrite the expression so that the GCF is factored completely. (3 points)

Part B: Rewrite the expression completely factored. Show the steps of your work. (4 points)

Part C: If the two middle terms were switched so that the expression became 3x3y - 3x2y + 12xy - 12y, would the factored expression no longer be equivalent to your answer in part B? Explain your reasoning. (3 points)

2. Part A: Write the expression x2 + 5x + 6 as a product of two linear expressions. Show your work and justify each step. (5 points) 

Part B: Rewrite x2 - 4x + 4 as a square of a linear expression. (3 points)

Part C: Do the expressions in parts A and B have a common factor? Justify your answer. (2 points)

3. Part A: The area of a square is (25x2 - 20x + 4) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (3 points) 

Part B: The area of a rectangle is (49x2 - 36y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (2 points)

Part C: The volume of a rectangular box is (x3 + 2x2 - 9x - 18) cubic units. Determine the dimensions of the rectangular box by factoring the volume expression completely. Show your work. (5 points)

4. An expression is shown below:

f(x) = -16x2 + 24x + 16

Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)

Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)

Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)

5. A function is shown below:

f(x) = x3 + 4x2 - x - 4

Part A: What are the factors of f(x)? Show your work. (3 points)

Part B: What are the zeros of f(x)? Show your work. (2 points)

Part C: What are the steps you would follow to graph f(x)? Describe the end behavior of the graph of f(x).