### 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)
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)
Part B: The area of a rectangle is (49×2- 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+ 2×2- 9x – 18) cubic units. Determine the dimensions of the rectangular box by factoring the volume expression completely. Show your work. (5 points)
f(x) = -16×2+ 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)
f(x) = x3+ 4×2- 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). 