Three students were asked to rewrite the expression 18x3 + 36x5 using a common factor. The rewritten expressions are shown in the table. Student A Student B Student C 4x3(4 + 9x2) 3x2(6x + 12x3) 9x3(2 + 4x2) Part A: Did Student A rewrite the expression correctly using a common factor? Explain. (3 points) Part B: Did Student B rewrite the expression correctly using a common factor? Explain. (3 points) Part C: Did Student C rewrite the expression correctly using a common factor? Explain. (3 points) Part D: Rewrite the expression using a different common factor than what is shown in the table. Choose a common factor that includes a coefficient other than 1 and a variable. Show every step of your work.

Answer 1

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)