Question

Please helppp i dont know what to do

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)

Answer 1

Only Student B factored the expression correctly by identifying x^3 as the common factor and writing it as 2x^3(14 + 10x^2). Student A and C did not correctly identify the greatest common factor. The expression can also be factored as 4x^3(7 + 5x^2).

Step-by-step explanation:

The question asks students to factorize the expression 28x3 + 20x5 using a common factor.

Part A: Student A

Student A rewrote the expression as 4x2(7x + 5x3). This is not completely correct because the common factor should also include the variable x to the smallest power present in both terms, which in this case is x3. The coefficient part is factored correctly.

Part B: Student B

Student B rewrote the expression as 2x3(14 + 10x2). This is correct, as they have identified x3 as the common factor for both terms and factored it out appropriately.

Part C: Student C

Student C rewrote the expression as 10x3(3 + 2x2). This is not correct because they have not factored out the greatest common factor. The largest common coefficient is 4, not 10.

Part D: Different Common Factor

To rewrite the expression using a different common factor, we can use 4x3 as the greatest common factor:

1. Factor out 4x3 from each term.
2. Rewrite the expression as 4x3(7 + 5x2).