Part A: Student A rewrote the expression correctly using the common factor of 18x3. They factored out 18x3 from both terms of the expression to get 18x3(1 + 2x2).
Part B: Student B did not rewrite the expression correctly using a common factor. They factored out 3x2 from the first term and 12x3 from the second term, which are not common factors. The correct common factor would be 18x3.
Part C: Student C rewrote the expression correctly using the common factor of 9x3. They factored out 9x3 from both terms of the expression to get 9x3(2 + 4x2).
Part D: A different common factor that could be used is 6x3.
18x3 + 36x5
= 6x3(3x2 + 6x4)
= 6x3(3x2(1 + 2x2))
= 18x3(1 + 2x2)