Factoring Polynomials: Sum and Difference of Cubes
Question 8 • Common Core Algebra I B-IC
The factorization of 8x3 – 125 is (2x – 5)(jx2 + kx + 25). What are the values of j and k?
Answer
j
j = 6 and k = –10
j
j = 8 and k = 10
j
j = 4 and k = 25
j
j = 4 and k = 10
Explanation
Recognize 8x³ − 125 as a difference of cubes: (2x)³ − 5³. Using a³ − b³ = (a − b)(a² + ab + b²), the second factor is 4x² + 10x + 25, so j = 4 and k = 10.
AI-written and checked against the verified answer.