2020 · Q32
The HCF and the LCM of two polynomials are 3x + 1 and 30x³ + 7x² − 10x − 3 respectively. If one polynomial is 6x² + 5x + 1, then what is the other polynomial?
Elementary MathematicsHCF and LCM
- A15x² + 4x + 3
- B15x² + 4x − 3
- C15x² − 4x + 3
- D15x² − 4x − 3
Explanation
The other polynomial is HCF*LCM divided by the given one: (3x+1)(30x^3+7x^2-10x-3)/(6x^2+5x+1). Since 6x^2+5x+1 = (3x+1)(2x+1), dividing the LCM by (2x+1) gives 15x^2-4x-3. Hence option (D).