Answers Algebra II Factoring Polynomials: Sum and Difference of Cubes — QuizQuestion 7

7

QuizMultiple Choice

Factoring Polynomials: Sum and Difference of Cubes — Quiz

Question 7 • Algebra II

Which product will result in a sum or difference of cubes?

Answer

A

open paren x minus 9 close paren times open paren x squared plus 9 x plus 81 close paren

B

open paren x minus 10 close paren times open paren x squared minus 10 x plus 100 close paren

C

open paren x plus 7 close paren times open paren x squared minus 7 x plus 14 close paren

D

open paren x plus 8 close paren times open paren x squared plus 8 x plus 64 close paren

Explanation

A difference of cubes factors as (a − b)(a² + ab + b²). Choice A matches this pattern with a = x and b = 9, so the product is x³ − 9³, or x³ − 729. The other choices do not have the required signs and middle terms for a sum or difference of cubes.

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