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

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).

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