Question

The polynomial 6x2 + x − 15 has a factor of 2x − 3. What is the other factor?


3x − 5
3x + 5
4x − 5
4x + 5

Answer 1

Let the other factor be ax + b. Then (2x − 3)(ax + b) = 6x^2 + x − 15.
Comparing coefficients: 2a = 6 → a = 3. Then 2b − 3a = 1 → 2b − 9 = 1 → b = 5.
So the other factor is 3x + 5.