Question

Anna wants to factor the polynomial p(x)=5x^4+40x. She knows that the sum of cubes formula is a^3+b^3=(a+b)(a^2−ab+b^2).

Anna decides to use the formula to factor the polynomial. First, she factors 5x out of the expression. Next, she identifies a and b. Finally, she factors the expression according to the formula.

5x^4+40x=5x(x^3+8)
a=x; b=8
5x^4+40x=5x(x+8)(x^2−8x+64)

Part A: Which statement correctly analyzes Anna’s work?

Part B: What is the correct factorization of the polynomial 5x^4+40x?

Select one answer for Part A and one answer for Part B.



1. B: 5x(x+8)(x^2−8x+64)

2 .A: Anna’s answer is incorrect. She correctly factored out 5x, but incorrectly identified a and b, so her answer cannot be correct.

3. B: 5x(x+2)(x^2−2x+4)

4. .B: (x+8)(x^2−8x+64)

5. A: Anna’s answer is incorrect. She correctly factored out 5x, correctly identified a and b, but did not use the formula correctly.

6. A: Anna’s answer is correct. She correctly factored out 5x, correctly identified a and b, and correctly used the formula.

7. A: Anna’s answer is incorrect. She should not have factored out 5x. Instead, she should have first identified a and b.

8. B: (x+2)(x^2−2x+4)

Answer 1

Part A: Option 2, A: Anna’s answer is incorrect. She correctly factored out 5x, but incorrectly identified a and b, so her answer cannot be correct.

Part B: Option 3, B: 5x(x+2)(x^2−2x+4)

Explanation:

p(x) = 5x^4 + 40x

p(x) = 5x(x^3 + 8)

p(x) = 5x(x + 2)(x^2 - 2x + 4)

Part A: Option 2, A: Anna’s answer is incorrect. She correctly factored out 5x, but incorrectly identified a and b, so her answer cannot be correct.

Part B: Option 3, B: 5x(x+2)(x^2−2x+4)