Question

Three students were asked to rewrite the expression 24x^3 + 36x^5 using a common factor. The rewritten expressions are shown in the table.

Student A Student B Student C
2x^2(12x + 18x^3) 6x^3(4 + 6x^2) 9x^3(3 + 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.

Answer 1

Student A did not rewrite the expression correctly using a common factor.

Student B and Student C both rewrote the expression correctly using a common factor.

An alternative common factor is 12x^3.

Step-by-step explanation:

Part A: Student A did not rewrite the expression correctly using a common factor. The common factor should be the highest power of x that divides evenly into both terms of the expression.

In this case, the common factor should be x^3, not x^2. The correct expression would be 24x^3(1 + 1.5x^2).

Part B: Student B did rewrite the expression correctly using a common factor. The common factor they used is 6x^3, which is the highest power of x that divides evenly into both terms of the expression.

The correct expression would be 6x^3(4 + 6x^2).

Part C: Student C did rewrite the expression correctly using a common factor. The common factor they used is 9x^3, which is the highest power of x that divides evenly into both terms of the expression.

The correct expression is 9x^3(3 + 4x^2).

Part D: If we want to rewrite the expression using a different common factor, we could use 12x^3 as the common factor. The expression would then be 12x^3(2x^2 + 3x^4).