Question

Three students were asked to rewrite the expression 36x3+ 16x5 using a common factor. The rewritten expressions are shown in the table. Student A Student B Student C 4x3(9 + 4x2) 3x2(12x + 2x3) 2x(18x2 + 8x4) 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. (3 points)

Answer 1

Part A- The correct expression would be 4x3(9 + 4x2).

Part B- The correct expression would be 16x5(3x2 + 2x3).

Part C- The correct expression would be 2x(18x2 + 8x4).

Part D- The correct expression would be 2x(18x2 + 8x4).

Step-by-step explanation:

Part A: No, Student A did not rewrite the expression correctly using a common factor. In the original expression, the common factor is 4x3, but Student A mistakenly distributed the factor instead of factoring it out. The correct expression would be 4x3(9 + 4x2).

Part B: No, Student B did not rewrite the expression correctly using a common factor. In the original expression, the common factor is 16x5, but Student B wrote 3x2(12x + 2x3) without factoring out the common factor. The correct expression would be 16x5(3x2 + 2x3).

Part C: Yes, Student C rewrote the expression correctly using a common factor. In the original expression, the common factor is 2x, and Student C factored it out correctly to get 2x(18x2 + 8x4).

Part D: To rewrite the expression using a different common factor, let's use 2x. We can factor out 2x from each term: 36x3 + 16x5 becomes 2x(18x2) + 2x(8x4). So the expression using the common factor 2x is 2x(18x2 + 8x4).