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.

Question

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)

Answer 2

Part A: Yes, Student A correctly rewrote the expression using a common factor. The common factor in their expression is 4x^3, which when factored out, leaves (4 + 9x^2). This means that the expression can be simplified as 4x^3(4 + 9x^2).

Part B: No, Student B did not rewrite the expression correctly using a common factor. The common factor they used is 3x^2, which is incorrect. They factored out the common factor incorrectly and left behind (6x + 12x^3) instead of simplifying it.

Part C: No, Student C did not rewrite the expression correctly using a common factor. The common factor they used is 9x^3, which is incorrect. They factored out the common factor incorrectly and left behind (2 + 4x^2) instead of simplifying it.

Part D: To rewrite the expression using a different common factor, let's use the common factor 6x^2. We can then factor out this common factor from the original expression 18x^3 + 36x^5:

18x^3 + 36x^5

Common factor: 6x^2

6x^2(3x + 6x^3)

So, using the common factor 6x^2, the expression can be rewritten as 6x^2(3x + 6x^3).