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CDS 2023 · PYQ · Algebra · medium

Which one of the following is a factor of a² − b² − c² + 2bc + a + b − c?

Answer

The correct answer is A: a−b−c+1. a²−(b−c)²+(a+b−c) = (a−b+c)(a+b−c)+(a+b−c) = (a+b−c)(a−b+c+1). So a−b+c+1 is a factor.

  1. A.a−b−c+1✓ Correct
  2. B.a+b+c−1
  3. C.a−b+c+1
  4. D.a+b+c+1

Explanation

a²−(b−c)²+(a+b−c) = (a−b+c)(a+b−c)+(a+b−c) = (a+b−c)(a−b+c+1). So a−b+c+1 is a factor.
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