2023 · Q75
Which one of the following is a factor of a² − b² − c² + 2bc + a + b − c?
Elementary MathematicsAlgebra
- Aa + b + c + 1
- Ba − b − c + 1
- Ca + b + c − 1
- Da − b + c + 1
Explanation
Group as a² − (b² − 2bc + c²) + (a + b − c) = a² − (b − c)² + (a + b − c). The first two terms form a difference of squares: (a − (b−c))(a + (b−c)) = (a − b + c)(a + b − c). Adding the remaining (a + b − c) and factoring it out gives (a + b − c)(a − b + c + 1). Hence (a − b + c + 1) is a factor, matching option (D).