2016 · Q7
The sum and difference of two expressions are 5x²-x-4 and x²+9x-10 respectively. The HCF of the two expressions will be
Elementary MathematicsAlgebra
- A(x+1)
- B(x-1)
- C(3x+7)
- D(2x-3)
Explanation
Adding the sum and difference: the first expression is E₁ = 3x²+4x−7 = (3x+7)(x−1), and the second is E₂ = 2x²−5x+3 = (2x−3)(x−1). Their greatest common divisor is the common factor (x−1), option B. The remaining factors (3x+7) and (2x−3) each divide only one expression, and (x+1) divides neither.