2021 · Q8
What is the sum of the linear factors (in x and y) of the expression 2x² + xy − 3y² ?
Elementary MathematicsAlgebra
- A2x − 3y
- B3x − 2y
- C3x + 2y
- D2x + 3y
Explanation
Factorising, 2x² + xy − 3y² = (2x + 3y)(x − y), which can be checked by expanding: 2x² − 2xy + 3xy − 3y². The linear factors in x and y are therefore (2x + 3y) and (x − y). Their sum is (2x + 3y) + (x − y) = 3x + 2y. This is option (c).