Mathematics, 14.03.2020 01:04 JamesLachoneus
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)
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