Question

PLEASE HURRY!!!!!!

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

Students B and C incorrectly factored the expression 28x³ + 20x⁵. Student B's factorization is correct, but Students A and C's are not, because when you multiply their factors, they don't reproduce the original expression. A new factorization with a coefficient other than 1 could be 4x³(7 + 5x²).

Step-by-step explanation:

The objective here is to determine if Students A, B, and C correctly factored the expression 28x³ + 20x⁵ by finding a common factor.

Part A: Student A wrote the expression as 4x²(7x+ 5x³). This is incorrect because when the expression inside the parentheses is multiplied by 4x², it does not reproduce the original expression.

Part B: Student B correctly factored the expression as 2x³(14 + 10x²). When the binomial is multiplied by 2x³, it will yield the original expression.

Part C: Student C has an error in factoring the expression as 10x³(3 + 2x²) because the coefficients when multiplied will not recreate the original expression.

Part D: To use a different common factor with a coefficient other than 1 and a variable, we can choose 4x³ as the common factor.

We then get 4x³(7 + 5x²).

Multiplying the binomial by 4x³ will give us the original expression: 28x³ + 20x⁵.