Three students were asked to rewrite the expression 28x3 + 20x5 using a common factor. The rewritten expressions are shown in the table.
Student A Student B Student C
4x2(7x+ 5x3) 2x3(14 + 10x2) 10x3(3 + 2x2)
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)
Part A:
Student A did rewrite the expression correctly using a common factor. They factored out the common factor of 4x2 from each term of the expression, resulting in 4x2(7x + 5x3).
Part B:
Student B did not rewrite the expression correctly using a common factor. They factored out the common factor of 2x3 from only the second term of the expression, resulting in 2x3(14 + 10x2). The first term remains unchanged.
Part C:
Student C did rewrite the expression correctly using a common factor. They factored out the common factor of 10x3 from each term of the expression, resulting in 10x3(3 + 2x2).
Part D:
To rewrite the expression using a different common factor, let's choose 2x as the common factor:
28x3 + 20x5
= 2x(14x2 + 10x4)
Here, we factored out the common factor of 2x from each term of the expression. The resulting expression is 2x(14x2 + 10x4).