9
QuizMultiple Choice

Factoring Polynomials: Sum and Difference of Cubes

Question 9 • Common Core Algebra I B-IC

Hank’s teacher asked him to verify that the product (y−3)(y2+3y+9) is a difference of cubes. He used the distributive property to multiply the binomial times the trinomial. Before simplifying, his product was a polynomial of the form y3+3y2+ay−3y2−ay−27. What is the value of a in the polynomial?

Answer
A
3
B
9
C
18
D
27

Explanation

Distribute each term in y − 3 across y² + 3y + 9. The product is y³ + 3y² + 9y − 3y² − 9y − 27. Comparing this with y³ + 3y² + ay − 3y² − ay − 27 shows that a = 9, so the correct choice is 9.

AI-written and checked against the verified answer.

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