Three students were asked to rewrite the expression 18x^3 + 36x^5 using a common factor. The rewritten expressions are shown in the table.
Student A:
4x^3(4 + 9x^2)
Student B:
3x^2(6x + 12x^3)
Student C:
9x^3(2 + 4x^2)
Part A: Did Student A rewrite the expression correctly using a common factor? Explain.
Part B: Did Student B rewrite the expression correctly using a common factor? Explain.
Part C: Did Student C rewrite the expression correctly using a common factor? Explain.
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.
Part A: Yes, Student A rewrote the expression correctly using a common factor. The common factor in their expression is 4x^3.
Part B: No, Student B did not rewrite the expression correctly using a common factor. The expression they provided does not factor out any common term.
Part C: No, Student C did not rewrite the expression correctly using a common factor. The expression they provided does not factor out any common term.
Part D: One possible common factor to rewrite the expression could be 6x^3.
18x^3 + 36x^5 can be rewritten as 6x^3(3 + 6x^2)